Dimensional regularization for zero‐mass particles in quantum field theory

1974 ◽  
Vol 15 (1) ◽  
pp. 82-85 ◽  
Author(s):  
D. M. Capper ◽  
G. Leibbrandt
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Dimensional Regularization ◽  
Quantum Field ◽  
Zero Mass

scholarly journals Quantum quench and thermalization to GGE in arbitrary dimensions and the odd-even effect

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Parijat Banerjee ◽  
Adwait Gaikwad ◽  
Anurag Kaushal ◽  
Gautam Mandal
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Power Law ◽  
Cold Atom ◽  
Quantum Field ◽  
Approach To Equilibrium ◽  
Zero Mass ◽  
Quantum Quench ◽  
Spatial Dimensions ◽  
Arbitrary Dimensions

Abstract In many quantum quench experiments involving cold atom systems the post-quench phase can be described by a quantum field theory of free scalars or fermions, typically in a box or in an external potential. We will study mass quench of free scalars in arbitrary spatial dimensions d with particular emphasis on the rate of relaxation to equilibrium. Local correlators expectedly equilibrate to GGE; for quench to zero mass, interestingly the rate of approach to equilibrium is exponential or power law depending on whether d is odd or even respectively. For quench to non-zero mass, the correlators relax to equilibrium by a cosine-modulated power law, for all spatial dimensions d, even or odd. We briefly discuss generalization to O(N ) models.

Renormalization

2021 ◽  
pp. 171-222
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Dimensional Regularization ◽  
General Concept ◽  
Feynman Diagrams ◽  
Quantum Field ◽  
Subtraction Procedure ◽  
Renormalization Group Equations

This chapter describes in detail the general concept of renormalization. It starts with a discussion of the regularization of Feynman diagrams. After that, the subtraction procedure is explained in detail, followed by an introduction to the notion of a superficial degree of divergence of the diagram. On this basis, the models of quantum field theory are classified as renormalizable or non-renormalizable theories. The main arbitrariness of the subtraction procedure is fixed by imposing renormalization conditions. Special sections of this chapter are devoted to renormalization in dimensional regularization and renormalization group equations.

Quantum field theory in de Sitter space: renormalization by point-splitting

1978 ◽  
Vol 360 (1700) ◽  
pp. 117-134 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Stress Tensor ◽  
Dimensional Regularization ◽  
De Sitter Space ◽  
Quantum Field ◽  
De Sitter ◽  
Point Splitting

We examine the modes of a scalar field in de Sitter space and construct quantum two-point functions. These are then used to compute a finite stress tensor by the technique of covariant point-splitting. We propose a renormalization ansatz based on the DeWitt-Schwinger expansion, and show that this removes all am biguities previously present in pointsplitting regularization. The results agree in detail with previous work by dimensional regularization, and give rise to an anomalous trace with the conventional coefficient. We describe how’ our treatment may be extended to more general situations.

scholarly journals Whether an Enormously Large Energy Density of the Quantum Vacuum Is Catastrophic

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 314 ◽  
Author(s):  
Vladimir Mostepanenko ◽  
Galina Klimchitskaya
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Energy Density ◽  
Cosmological Constant ◽  
Dimensional Regularization ◽  
Gravitational Effect ◽  
Large Energy ◽  
Physical Parameters ◽  
Quantum Field ◽  
Quantum Vacuum

The problem of an enormously large energy density of the quantum vacuum is discussed in connection with the concept of renormalization of physical parameters in quantum field theory. Using the method of dimensional regularization, it is recalled that the normal ordering procedure of creation and annihilation operators is equivalent to a renormalization of the cosmological constant leading to its zero and nonzero values in Minkowski space-time and in the standard cosmological model, respectively. It is argued that a frequently discussed gravitational effect, resulting from an enormously large energy density described by the nonrenormalized (bare) cosmological constant, might be nonobservable much like some other bare quantities introduced in the formalism of quantum field theory.

Finite massless quantum field theory

1992 ◽  
Vol 70 (6) ◽  
pp. 463-466
Author(s):  
A. Y. Shiekh
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Analytic Continuation ◽  
Dimensional Regularization ◽  
Quantum Field ◽  
Four Dimensions ◽  
Infrared Divergences ◽  
Massless Quantum

Massless quantum field theory is usually troubled by both ultraviolet and infrared divergences. With the help of analytic continuation, this fact can be exploited to eliminate, or at least reduce the overall number of divergences. This mechanism is investigated within the context of dimensional regularization for the case of massless [Formula: see text] theory in four dimensions.

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