Physics
Quantum Field Theory
Quantum Field Theory is a theoretical framework that combines quantum mechanics with special relativity to describe the behavior of subatomic particles. It treats particles as excited states of underlying fields, and interactions between particles are described in terms of exchanges of other particles. Quantum Field Theory has been successful in predicting and explaining a wide range of phenomena in particle physics.
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11 Key excerpts on "Quantum Field Theory"
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter 1 Introduction to Quantum Field Theory Quantum Field Theory ( QFT ) provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized (represented) by an infinite number of dynamical degrees of freedom, that is, fields and (in a condensed matter context) many-body systems. It is the natural and quantitative language of particle physics and condensed matter physics. Most theories in modern particle physics, including the Standard Model of elementary particles and their interactions, are formulated as relativistic quantum field theories. Quantum field theories are used in many contexts, elementary particle physics being the most vital example, where the particle count/number going into a reaction fluctuates and changes, differing from the count/number going out, for example, and for the description of critical phenomena and quantum phase transitions, such as in the BCS theory of superconductivity, also see phase transition, quantum phase transition, critical phenomena. Quantum Field Theory is thought by many to be the unique and correct outcome of combining the rules of quantum mechanics with special relativity. In perturbative Quantum Field Theory, the forces between particles are mediated by other particles. The electromagnetic force between two electrons is caused by an exchange of photons. Intermediate vector bosons mediate the weak force and gluons mediate the strong force. There is currently no complete quantum theory of the remaining fundamental force, gravity, but many of the proposed theories postulate the existence of a graviton particle that mediates it. These force-carrying particles are virtual particles and, by definition, cannot be detected while carrying the force, because such detection will imply that the force is not being carried.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter 3 Quantum Field Theory Quantum Field Theory ( QFT ) provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized (represented) by an infinite number of dynamical degrees of freedom, that is, fields and (in a condensed matter context) many-body systems. It is the natural and quantitative language of particle physics and condensed matter physics. Most theories in modern particle physics, including the Standard Model of elementary particles and their interactions, are form-ulated as relativistic quantum field theories. Quantum field theories are used in many contexts, elementary particle physics being the most vital example, where the particle count/number going into a reaction fluctuates and changes, differing from the count/ number going out, for example, and for the description of critical phenomena and quantum phase transitions, such as in the BCS theory of superconductivity, also see phase transition, quantum phase transition, critical phenomena. Quantum Field Theory is thought by many to be the unique and correct outcome of combining the rules of quantum mechanics with special relativity. In perturbative Quantum Field Theory, the forces between particles are mediated by other particles. The electromagnetic force between two electrons is caused by an exchange of photons. Intermediate vector bosons mediate the weak force and gluons mediate the strong force. There is currently no complete quantum theory of the remaining funda-mental force, gravity, but many of the proposed theories postulate the existence of a graviton particle that mediates it. These force-carrying particles are virtual particles and, by definition, cannot be detected while carrying the force, because such detection will imply that the force is not being carried.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- White Word Publications(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter 4 Quantum Field Theory Quantum Field Theory ( QFT ) provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized (represented) by an infinite number of dynamical degrees of freedom, that is, fields and (in a condensed matter context) many-body systems. It is the natural and quantitative language of particle physics and condensed matter physics. Most theories in modern particle physics, including the Standard Model of elementary particles and their interactions, are formulated as relativistic quantum field theories. Quantum field theories are used in many contexts, elementary particle physics being the most vital example, where the particle count/number going into a reaction fluctuates and changes, differing from the count/number going out, for example, and for the description of critical phenomena and quantum phase transitions, such as in the BCS theory of superconductivity, also see phase transition, quantum phase transition, critical phenomena. Quantum Field Theory is thought by many to be the unique and correct outcome of combining the rules of quantum mechanics with special relativity. In perturbative Quantum Field Theory, the forces between particles are mediated by other particles. The electromagnetic force between two electrons is caused by an exchange of photons. Intermediate vector bosons mediate the weak force and gluons mediate the strong force. There is currently no complete quantum theory of the remaining fundamental force, gravity, but many of the proposed theories postulate the existence of a graviton particle that mediates it. These force-carrying particles are virtual particles and, by definition, cannot be detected while carrying the force, because such detection will imply that the force is not being carried.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 3 Quantum Field Theory Quantum Field Theory ( QFT ) provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized (represented) by an infinite number of dynamical degrees of freedom, that is, fields and (in a condensed matter context) many-body systems. It is the natural and quantitative language of particle physics and condensed matter physics. Most theories in modern particle physics, including the Standard Model of elementary particles and their interactions, are formulated as relativistic quantum field theories. Quantum field theories are used in many contexts, elementary particle physics being the most vital example, where the particle count/number going into a reaction fluctuates and changes, differing from the count/number going out, for example, and for the description of critical phenomena and quantum phase transitions, such as in the BCS theory of superconductivity. Quantum Field Theory is thought by many to be the unique and correct outcome of combining the rules of quantum mechanics with special relativity. In perturbative Quantum Field Theory, the forces between particles are mediated by other particles. The electromagnetic force between two electrons is caused by an exchange of photons. Intermediate vector bosons mediate the weak force and gluons mediate the strong force. There is currently no complete quantum theory of the remaining fundamental force, gravity, but many of the proposed theories postulate the existence of a graviton particle that mediates it. These force-carrying particles are virtual particles and, by definition, cannot be detected while carrying the force, because such detection will imply that the force is not being carried. In addition, the notion of force mediating particle comes from perturbation theory, and thus does not make sense in a context of bound states.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Library Press(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 4 Quantum Field Theory Quantum Field Theory ( QFT ) provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized (represented) by an infinite number of dynamical degrees of freedom, that is, fields and (in a condensed matter context) many-body systems. It is the natural and quantitative language of particle physics and condensed matter physics . Most theories in modern particle physics, including the Standard Model of elementary particles and their interactions, are formulated as relativistic quantum field theories. Quantum field theories are used in many contexts, elementary particle physics being the most vital example, where the particle count/number going into a reaction fluctuates and changes, differing from the count/number going out, for example, and for the description of critical phenomena and quantum phase transitions, such as in the BCS theory of superconductivity. Quantum Field Theory is thought by many to be the unique and correct outcome of combining the rules of quantum mechanics with special relativity. In perturbative Quantum Field Theory, the forces between particles are mediated by other particles. The electromagnetic force between two electrons is caused by an exchange of photons. Intermediate vector bosons mediate the weak force and gluons mediate the strong force. There is currently no complete quantum theory of the remaining fundamental force, gravity , but many of the proposed theories postulate the existence of a graviton particle that mediates it. These force-carrying particles are virtual particles and, by definition, cannot be detected while carrying the force, because such detection will imply that the force is not being carried. In addition, the notion of force mediating particle comes from perturbation theory, and thus d oes not make sense in a context of bound states.
eBook - PDF- Anthony Zee(Author)
- 2023(Publication Date)
- Princeton University Press(Publisher)
P A R T V Quantum Field Theory and the four fundamental interactions Preview of part V Since Quantum Field Theory was developed to address the wealth of peculiar phenomena that appeared at the confluence of special relativity and quan- tum physics, its development was naturally intertwined with the development of particle physics, also known as high energy physics. But just as atomic physics is not synonymous with quantum mechanics, particle physics is not synonymous with Quantum Field Theory. We will start with one of the most striking predictions of quantum field the- ory, the existence of antimatter. Then we will explore the strong and the weak interactions in turn. The electromagnetic interaction, in contrast to these two, nurtured the growth of Quantum Field Theory and so has already been focused on in the earlier parts of this book. I then explain electroweak unification. This is followed by the exciting possibility of grand unification, by which three of the four fundamental interactions may be unified into a single interaction. Finally, we turn to quantum gravity as a Quantum Field Theory. Since particle physics is by itself an extraordinarily rich subject, with each of the four interactions easily occupying an entire book, I have to cut even more corners than before, echoing Feynman’s warning cited in the preface. １８６ Preview of part V A more casual reader may wish to read only chapter V.1 in detail and then skim the rest of this part to obtain a flavor of how we have gotten to our present understanding of the four fundamental interactions. It is also possible, or perhaps even advisable for some readers, to skip ahead to part VI and come back to this part later at your leisure.
- Paul Teller(Author)
- 2020(Publication Date)
- Princeton University Press(Publisher)
C H A P T E R F O U R Free Quantum Field Theory FIELD THEORIES FREE Quantum Field Theory is the theory of quantum fields in which the effect of interactions is entirely neglected. But we had better start by saying what we mean by a field theory. A field theory presupposes a continuum of space-time points. This involves a number of technical considerations that do not concern us here. (The continuum constitutes a differentiable manifold, which can be described by coordinates and to which an affine connection and a metric can be assigned.) The idea of a field enters as the idea that values of physical quantities can be attributed to the space-time points. Specification of the values of all relevant quantities to each space-time point specifies a configuration of the field. And we have a field theory insofar as we have field equations, that is, laws, usually in the form of differential equations, constraining the values of quantities at different space-time points. I want to focus on the idea that values of various quantities can be attributed to the space-time points. In any specific case we talk about such attribution in much the way we talk about predication of simple properties: One attributes a humdrum property (for example, the color red) to an object (for example, my shirt) by associating a predicate (the word, 'red') with a referring expression ('my shirt'). Similarly, in describing the value of a field quantity (for example, a gravitational potential) at a point, one associates a mathematical entity (for example, a real number) representing the value of the quantity with numerical coordinates representing the point. What kinds of quantities can be attributed to the space-time points? We know familiar examples in the form of scalars (a matter density, a gravitational potential), vectors (electric and magnetic fields), and higher-order tensors (the stress-energy tensor).
eBook - PDF- Eugene Stefanovich(Author)
- 2018(Publication Date)
- De Gruyter(Publisher)
19 Thus any QFT is doomed to suffer 18 It should be noted that a similar situation takes place in nonrelativistic theories, for example, in solid-state physics, where the continuous quantum field description is really approximate and only works within the limits of low energies and large distances. For example, the quantum field description of crystal lattice vibrations in terms of phonons is applicable only when deviations of atoms from their equilibrium positions are much smaller than interatomic distances. The concept of renormalization is also physically justified in these theories. For example, the polaron ( = the electron moving through the crystal while interacting with lattice vibrations) has a renormalized mass that differs from the effective mass of the electron in the conduction band of the “fixed” lattice. In this book we discuss only fundamental relativistic quantum fields where such considerations and analogies are inapplicable. 19 Indeed, any quantum field is a sum of creation and annihilation parts ϕ ∝ ( α † + α ) . In field theories, interaction is built as a polynomial in quantum fields (see Section 2 -3.1), and any field monomial would 8 | 1 Three ways to look at QFT from renormalization problems. These problems are much deeper than just the diver-gence of loop integrals. The redefinition of the vacuum and one-particle states would be necessary even if all loop integrals were convergent. 1.2.1 A bit of history The idea of clothed particles has a long history. Van Hove was the first to express his thoughts about “persistent perturbations” in QFT [257, 258]. The first clear formula-tion of the clothed-particle concept and its application to model QFTs is contained in the excellent article by Greenberg and Schweber [101]. This formalism was extended to various quantum field models, including the scalar-field model [265], the Lee model [73, 83, 54, 55, 6] and the Ruijgrok–Van Hove model [202, 159].
- Tian Yu Cao(Author)
- 2019(Publication Date)
- Cambridge University Press(Publisher)
All such quanta, as distinct from classical permanent particles, can be created and destroyed. So this is a field theory not only in the sense that the agents for transmitting interaction between particles are field quanta, but also in the sense that the interacting particles themselves should be viewed as manifestations of fields. In addition, a fermion field (such as the electron–positron field) can also transmit interactions via its quanta just like the electromagnetic field via photons. Thus the distinc- tion between matter and force field vanishes from the scene, and is to be replaced by a universal particle–field duality affecting equally each of the constituent entities. Quantum electrodynamics, based on the works of Jordan (with Born, 1925, with Born and Heisenberg, 1926), Dirac (1927b, c, 1928a, b, 1930a, 1931), Jordan and Wigner (1928), and Heisenberg and Pauli (1929, 1930), 18 was a starting point from which the 156 The Formation of the Conceptual Foundations of QFT quantum theories of interactions have developed along two lines. One led to Fermi’s theory of beta decay, the prototype of the quantum theory of weak interactions, and to Yukawa’s theory of mesons, the prototype of the quantum theory of strong interactions. The other led to gauge theories. The rest of this section is devoted to the first development, while the second line will be dealt with in Part III. The early development of the quantum theory of interactions was closely intertwined with nuclear physics. In fact, nuclear beta decay and the nuclear force that stabilizes the nucleus were two topics which provided the main stimulus to the development of novel ideas of interaction.
eBook - PDFThe Ultimate Constituents of the Material World
In Search of an Ontology for Fundamental Physics
- Meinard Kuhlmann(Author)
- 2013(Publication Date)
- De Gruyter(Publisher)
Part I Ontology and Quantum Field Theory Chapter 1 Introduction Since the very beginning of western philosophy reflections about the ma-terial world which go beyond the directly observable play a central role in philosophy. Starting with the presocratics it has always been a point of debate what the fundamental characteristics of the material world are. Is everything constantly changing or are there certain permanent features? What is basic and what is merely a matter of perspective and appearance? In the course of time various answers have been given and conflicting views have often been alternating in their predominance. Quantum Field The-ory (QFT)—the mathematical and conceptual framework for contempo-rary elementary particle physics—is presently the best starting point for analysing the fundamental features of matter and interactions. During the last two decades QFT became a more and more vividly discussed topic in the philosophy of physics. Since mathematical reasoning dominated the heuristics of QFT, its interpretation is still open in most areas which go beyond immediate empirical predictions. Philosophical analysis can help to clarify its semantics. QFT taken seriously in its metaphysical implica-tions seems to give a picture of the world which is at variance with central classical conceptions like particles and fields and even with some features of (non-relativistic) quantum mechanics. An ontological analysis of QFT can yield crucial insights about the fundamental properties of the material world. Which questions will be explored? The philosophical topic of this book is ontology, the investigation of the most general structures of what there is in the world. I will ask which kinds of things and modes of being there are in a very general sense. However, I will explore these issues 1 2 CHAPTER 1. INTRODUCTION mostly in relation to modern physics.
eBook - PDFQuantum Field Theory
From Operators to Path Integrals
- Kerson Huang(Author)
- 2008(Publication Date)
- Wiley-VCH(Publisher)
General properties of the quantum field will be discussed more fully in Chapter 2 . 1.3 SECOND QUANTIZATION Another way to obtain a quantum field is to consider a collection of identical parti- cles in quantum mechanics. In this case, the quantum field is an equivalent descrip- tion of the system. Identical particles are defined by a Hamiltonian that is (1) invari- ant under a permutation of the particle coordinates and ( 2 ) has the same form for any number of particles. The quantized-field description is called “second quantiza- tion” for historical reasons, but quantization was actually done only once. Let HN be the Hilbert space of a system of N identical nonrelativistic particles. The union of all gN is called the Fock space: CLI S = U % N=O (1.39) The subspace with N = 0 contains the vac~~um state as its only member. We assume that N is the eigenvalues of a “number operator” Nop, which commutes with the Hamiltonian. It is natural to introduce operators on Fock space that connect sub- spaces of different N. An elementary operator of this kind creates or annihilates one particle at a point in space. Such an operator is a quantum field operator, since it is a spatial function. This is why a quantum-mechanical many-particle system auto- matically gives rise to a quantum field. For definiteness, consider N nonrelativistic particles in three spatial dimen- sions, with coordinates {r,, . . . , rN}. The Hamiltonian is (1.40) where Ot is the Laplacian with respect to r,, and where V is a symmetric function of its arguments. The eigenfunctions Tn are defined by 8 Introducing Quantum Fields For Bose or Fermi statistics, qn is respectively symmetric or antisymmetric under an interchange of any two coordinates rr and r,. The particles are called bosons or fermions, respectively. We now describe the equivalent Quantum Field Theory, and justify it later. Let ~ r ) be the Schrodinger-picture operator that annihilates one particle at r.
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