Quantum Field Theory Methods: Dirac Equation and Perturbation Theory

1997 ◽  
pp. 447-478
Author(s):  
Urjit Yajnik
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Dirac Equation ◽  
Quantum Field

scholarly journals CAUSAL PERTURBATION THEORY IN TERMS OF RETARDED PRODUCTS, AND A PROOF OF THE ACTION WARD IDENTITY

2004 ◽  
Vol 16 (10) ◽  
pp. 1291-1348 ◽  
Author(s):  
MICHAEL DÜTSCH ◽  
KLAUS FREDENHAGEN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Ward Identity ◽  
Quantum Field ◽  
Algebraic Quantum Field Theory ◽  
Algebraic Quantum ◽  
Local Construction ◽  
Free Parameters ◽  
Classical Fields

In the framework of perturbative algebraic quantum field theory a local construction of interacting fields in terms of retarded products is performed, based on earlier work of Steinmann [42]. In our formalism the entries of the retarded products are local functionals of the off-shell classical fields, and we prove that the interacting fields depend only on the action and not on terms in the Lagrangian which are total derivatives, thus providing a proof of Stora's "Action Ward Identity" [45]. The theory depends on free parameters which flow under the renormalization group. This flow can be derived in our local framework independently of the infrared behavior, as was first established by Hollands and Wald [32]. We explicitly compute non-trivial examples for the renormalization of the interaction and the field.

scholarly journals Hadron physics from lattice QCD

2016 ◽  
Vol 25 (07) ◽  
pp. 1642008 ◽  
Author(s):  
Wolfgang Bietenholz
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Quantum Field ◽  
Chiral Perturbation ◽  
Hadron Physics ◽  
Lattice Regularization ◽  
Sign Problem ◽  
Hadron Masses ◽  
Basic Ideas

We sketch the basic ideas of the lattice regularization in Quantum Field Theory, the corresponding Monte Carlo simulations, and applications to Quantum Chromodynamics (QCD). This approach enables the numerical measurement of observables at the non-perturbative level. We comment on selected results, with a focus on hadron masses and the link to Chiral Perturbation Theory. At last, we address two outstanding issues: topological freezing and the sign problem.

Some quantum field theory aspects of the superspace quantization of general relativity

1976 ◽  
Vol 351 (1665) ◽  
pp. 209-232 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
General Relativity ◽  
Perturbation Theory ◽  
Constraint Equation ◽  
Mathematical Structure ◽  
Quantum Field ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
The Status

An investigation is started into a possible mathematical structure of the Wheeler-DeWitt superspace quantization of general relativity. The emphasis is placed throughout on quantum field theory aspects of the problem and topics discussed include canonical commutation relations in a triad basis, the status of the constraint equation and the rôle played by perturbation theory.

Quantum Field Theory

2020 ◽  
pp. 237-288
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Canonical Quantization ◽  
Feynman Diagrams ◽  
Field Theories ◽  
Coordinate Space ◽  
Matrix Formalism ◽  
Quantum Field ◽  
Transfer Matrix Formalism

Chapter 7 covers the main reasons for adopting the methods of quantum field theory (QFT) to study the critical phenomena. It presents both the canonical quantization and the path integral formulation of the field theories as well as the analysis of the perturbation theory. The chapter also covers transfer matrix formalism and the Euclidean aspects of QFT, the field theory of the Ising model, Feynman diagrams, correlation functions in coordinate space, the Minkowski space and the Legendre transformation and vertex functions. Everything in this chapter will be needed sooner or later, since it highlights most of the relevant aspects of quantum field theory.

Renormalization Group: From a general concept to numbers

2019 ◽  
pp. 69-80
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Renormalization Group ◽  
General Concept ◽  
Quantum Field ◽  
Fixed Dimension ◽  
Perturbative Renormalization ◽  
Borel Transformation

Chapter 5 first recalls the importance of the concept of scale decoupling in physics. It then emphasizes that quantum field theory and the theory of critical phenomena have provided two examples where this concepts fails. To deal with such a situation, a new tool has been invented: the renormalization group. In the framework of effective quantum field theory, a perturbative renormalization group has been formulated. Its implementation has led to the discovery of fixed points as zeros of beta functions, and calculations of critical exponents of a class of macroscopic phase transitions in the form of Wilson–Fisher epsilon or fixed dimension expansions. These expansions being divergent, they could summed by methods based on the Borel transformation and the determination of the large order behaviour of perturbation theory.

scholarly journals g-FUNCTION IN PERTURBATION THEORY

2004 ◽  
Vol 19 (15) ◽  
pp. 2545-2559
Author(s):  
ANATOLY KONECHNY
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Beta Function ◽  
Open String ◽  
Quantum Field ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
The Given

We present some explicit computations checking a particular form of gradient formula for a boundary beta function in two-dimensional quantum field theory on a disk. The form of the potential function and metric that we consider were introduced in Refs. 16 and 18 in the context of background independent open string field theory. We check the gradient formula to the third order in perturbation theory around a fixed point. Special consideration is given to situations when resonant terms are present exhibiting logarithmic divergences and universal nonlinearities in beta functions. The gradient formula is found to work to the given order.

scholarly journals Some differences between Dirac's hole theory and quantum field theory

2005 ◽  
Vol 83 (3) ◽  
pp. 257-271 ◽  
Author(s):  
Dan Solomon
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Exact Solution ◽  
Dirac Equation ◽  
Vacuum Energy ◽  
Time Dependent ◽  
Quantum Field ◽  
Hole Theory

Dirac's hole theory (HT) and quantum field theory (QFT) are generally considered equivalent. However, it was recently shown by several investigators that this is not necessarily the case because when the change in the vacuum energy was calculated for a time-independent perturbation, HT and QFT yielded different results. In this paper, we extend this discussion to include a time-dependent perturbation for which the exact solution to the Dirac equation is known. We show that for this case also, HT and QFT yield different results. In addition, we offer some discussion of the problem of anomalies in QFT. PACS Nos.: 03.65–w, 11.10–z

scholarly journals Singular structure of the QED effective action

2019 ◽  
Vol 49 ◽  
pp. 1960006
Author(s):  
B. A. Fayzullaev
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Singular Perturbation ◽  
Effective Action ◽  
Electromagnetic Interaction ◽  
Perturbation Series ◽  
Singular Perturbation Theory ◽  
Quantum Field ◽  
Coupling Constant

The equations for the QED effective action derived in Ref. 3 are considered using singular perturbation theory. The effective action is divided into regular and singular (in coupling constant) parts. It is shown that expression for the regular part coincides with usual Feynman perturbation series over coupling constant, while the remainder has essential singularity at the vanishing coupling constant: [Formula: see text]. This means that in the frame of quantum field theory it is impossible “to switch off” electromagnetic interaction in general and pass on to “free electron”.

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