scholarly journals A NOTE ON THE HEAT KERNEL METHOD APPLIED TO FERMIONS

2001 ◽  
Vol 16 (38) ◽  
pp. 2463-2468 ◽  
Author(s):  
G. DE BERREDO-PEIXOTO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Vector Fields ◽  
Kernel Method ◽  
Axial Vector ◽  
Constant Factor ◽  
Fermion Mass ◽  
Quantum Field ◽  
Fermionic Operators ◽  
Important Object

The spectrum of the fermionic operators depending on external fields is an important object in quantum field theory. In this paper we prove, using transition to the alternative basis for the γ-matrices, that this spectrum does not depend on the sign of the fermion mass, up to a constant factor. This assumption has been extensively used, but usually without proof. As an illustration, we calculated the coincidence limit of the coefficient a2(x,x′) on the general background of metric, vector and axial vector fields.

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.

Quantum field theory in curved space-time. Massive and massless vector fields

1981 ◽  
Vol 24 (10) ◽  
pp. 2576-2585 ◽  
Author(s):  
H. Ceccatto ◽  
A. Foussats ◽  
H. Giacomini ◽  
O. Zandron
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Vector Fields ◽  
Space Time ◽  
Quantum Field ◽  
Curved Space

Introduction to Quantum Field Theory

2019 ◽  
Author(s):  
Horatiu Nastase
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Cross Sections ◽  
Quantum Electrodynamics ◽  
Particle Physics ◽  
Vector Fields ◽  
Quantum Field ◽  
Fermionic Fields ◽  
Key Aspects ◽  
Scattering Cross Sections

Quantum Field Theory provides a theoretical framework for understanding fields and the particles associated with them, and is the basis of particle physics and condensed matter research. This graduate level textbook provides a comprehensive introduction to quantum field theory, giving equal emphasis to operator and path integral formalisms. It covers modern research such as helicity spinors, BCFW construction and generalized unitarity cuts; as well as treating advanced topics including BRST quantization, loop equations, and finite temperature field theory. Various quantum fields are described, including scalar and fermionic fields, Abelian vector fields and Quantum ElectroDynamics (QED), and finally non-Abelian vector fields and Quantum ChromoDynamics (QCD). Applications to scattering cross sections in QED and QCD are also described. Each chapter ends with exercises and an important concepts section, allowing students to identify the key aspects of the chapter and test their understanding.

scholarly journals Representation of quantum field theory in an extended spin space and fermion mass hierarchy

2014 ◽  
Vol 29 (29) ◽  
pp. 1450144 ◽  
Author(s):  
J. Besprosvany ◽  
R. Romero
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Fermion Mass ◽  
Mass Hierarchy ◽  
Quantum Field ◽  
Spin Space ◽  
Matrix Space ◽  
Gauge Invariant ◽  
Spin Degree ◽  
Symmetry Operators

We consider a matrix space based on the spin degree of freedom, describing both a Hilbert state space and its corresponding symmetry operators. Under the requirement that the Lorentz symmetry be kept, at given dimension, scalar symmetries and their representations are determined. Symmetries are flavor or gauge-like, with fixed chirality. After spin 0, 1/2 and 1 fields are obtained in this space, we construct associated interactive gauge-invariant renormalizable terms, showing their equivalence to a Lagrangian formulation, using as example the previously studied (5+1)-dimensional case, with many standard-model connections. At 7+1 dimensions, a pair of Higgs-like scalar Lagrangian is obtained naturally producing mass hierarchy within a fermion flavor doublet.

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