Anomalies in finite amplitudes: Two-dimensional single and triple axial-vector triangles

2018 ◽  
Vol 33 (23) ◽  
pp. 1850136
Author(s):  
O. A. Battistel ◽  
F. Traboussy ◽  
G. Dallabona
Keyword(s):  
Field Theory ◽  
Axial Vector ◽  
Space Time ◽  
Point Of View ◽  
Quantum Field ◽  
Two Dimensional ◽  
Point Function ◽  
Four Dimensions ◽  
Clear Point ◽  
A Chain

An explicit and detailed investigation about the two-dimensional (2D) single and triple axial-vector triangles is presented. Such amplitudes are related to the 2D axial-vector two-point function (AV) through contractions with the external momenta. Given this fact, before considering the triangles, we give a clear point of view for the AV anomalous amplitude. Such point of view is constructed within the context of an alternative strategy to handle the divergences typical of the perturbative solutions of quantum field theory. In the referred procedure all amplitudes in all theories, formulated in odd and even space–time dimensions, renormalizable or not, are treated on the same footing. After performing, in a very detailed way, all the calculations, we conclude that the same phenomenon occurring in the AV amplitude is present also in the finite single and triple axial-vector triangles. The conclusion gives support to the thesis that the phenomenon is present in pseudo-amplitudes belonging to a chain where the divergent AV one is only the simplest structure. It is expected that the same must occur in all even space–time dimensions. In particular, in four dimensions, the single and triple axial box amplitudes must exhibit anomalies too.

Massive quantum field theory in two-dimensional Robertson-Walker space-time

1978 ◽  
Vol 18 (12) ◽  
pp. 4435-4459 ◽  
Author(s):  
T. S. Bunch ◽  
S. M. Christensen ◽  
S. A. Fulling
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Space Time ◽  
Quantum Field ◽  
Two Dimensional

DOES STOCHASTIC ANALYTIC REGULARIZATION PROVIDE QUANTUM FIELD THEORIES?

1992 ◽  
Vol 07 (04) ◽  
pp. 777-794
Author(s):  
C. P. MARTIN
Keyword(s):  
Field Theory ◽  
Regularization Method ◽  
Gauge Theories ◽  
Field Theories ◽  
Intermediate Step ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Point Function ◽  
Four Dimensions ◽  
Analytic Regularization

We analyze whether the so-called method of stochastic analytic regularization is suitable as an intermediate step for constructing perturbative renormalized quantum field theories. We choose a λϕ3 in six dimensions to prove that this regularization method does not in general provide a quantum field theory. This result seems to apply to any field theory with a quadratically UV-divergent stochastic two-point function, for instance λϕ4 and gauge theories in four dimensions.

scholarly journals A new approach to anomalous axial vector field theory – II

2021 ◽  
pp. 2150155
Author(s):  
A. K. Kapoor
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Vector Field ◽  
Axial Vector ◽  
Quantum Field ◽  
Stochastic Quantization ◽  
New Approach ◽  
Four Dimensions

This work is continuation of a stochastic quantization program reported earlier. In this paper, we propose a consistent scheme of doing computations directly in four dimensions using conventional quantum field theory methods.

scholarly journals Exact four-point function and OPE for an interacting quantum field theory with space/time anisotropic scale invariance

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Hidehiko Shimada ◽  
Hirohiko Shimada
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scale Invariance ◽  
Asymptotic Series ◽  
Space Time ◽  
Quantum Field ◽  
Coupling Constant ◽  
Point Function ◽  
Calogero Model ◽  
Primary Operator

Abstract We identify a nontrivial yet tractable quantum field theory model with space/time anisotropic scale invariance, for which one can exactly compute certain four-point correlation functions and their decompositions via the operator-product expansion(OPE). The model is the Calogero model, non-relativistic particles interacting with a pair potential $$ \frac{g}{{\left|x-y\right|}^2} $$ g x − y 2 in one dimension, considered as a quantum field theory in one space and one time dimension via the second quantisation. This model has the anisotropic scale symmetry with the anisotropy exponent z = 2. The symmetry is also enhanced to the Schrödinger symmetry. The model has one coupling constant g and thus provides an example of a fixed line in the renormalisation group flow of anisotropic theories.We exactly compute a nontrivial four-point function of the fundamental fields of the theory. We decompose the four-point function via OPE in two different ways, thereby explicitly verifying the associativity of OPE for the first time for an interacting quantum field theory with anisotropic scale invariance. From the decompositions, one can read off the OPE coefficients and the scaling dimensions of the operators appearing in the intermediate channels. One of the decompositions is given by a convergent series, and only one primary operator and its descendants appear in the OPE. The scaling dimension of the primary operator we computed depends on the coupling constant. The dimension correctly reproduces the value expected from the well-known spectrum of the Calogero model combined with the so-called state-operator map which is valid for theories with the Schrödinger symmetry. The other decomposition is given by an asymptotic series. The asymptotic series comes with exponentially small correction terms, which also have a natural interpretation in terms of OPE.

scholarly journals ε-EXPANSION IN QUANTUM FIELD THEORY IN CURVED SPACE–TIME

1998 ◽  
Vol 13 (16) ◽  
pp. 2857-2874
Author(s):  
IVER H. BREVIK ◽  
HERNÁN OCAMPO ◽  
SERGEI ODINTSOV
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Space Time ◽  
Quantum Field ◽  
Curved Space ◽  
Njl Model ◽  
Effective Lagrangian ◽  
Special Solutions ◽  
Curvature Approximation ◽  
Symmetric Phase

We discuss ε-expansion in curved space–time for asymptotically free and asymptotically nonfree theories. The existence of stable and unstable fixed points is investigated for fϕ4 theory and SU(2) gauge theory. It is shown that ε-expansion maybe compatible with aysmptotic freedom on special solutions of the RG equations in a special ase (supersymmetric theory). Using ε-expansion RG technique, the effective Lagrangian for covariantly constant gauge SU(2) field and effective potential for gauged NJL model are found in (4-ε)-dimensional curved space (in linear curvature approximation). The curvature-induced phase transitions from symmetric phase to asymmetric phase (chromomagnetic vacuum and chiral symmetry broken phase, respectively) are discussed for the above two models.

Sign in / Sign up

Export Citation Format

Share Document