scholarly journals Gauge anomaly with vector and axial-vector fields in 6D curved space

2018 ◽  
Vol 2018 (3) ◽  
Author(s):  
Satoshi Yajima ◽  
Kohei Eguchi ◽  
Makoto Fukuda ◽  
Tomonori Oka
Keyword(s):  
Vector Fields ◽  
Axial Vector ◽  
Curved Space ◽  
Gauge Anomaly

Classical fields in curved spacetime

2021 ◽  
pp. 294-313
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Vector Fields ◽  
Lorentz Invariance ◽  
Conformal Symmetry ◽  
Scalar Fields ◽  
Gauge Fields ◽  
Curved Spacetime ◽  
Curved Space ◽  
Spinor Fields ◽  
Vector Gauge ◽  
Classical Fields

This chapter discusses classical fields in an arbitrary Riemann spacetime. General considerations are followed by the formulation of scalar fields with non-minimal coupling. Spontaneous symmetry breaking in curved space is shown to provide the induced gravity action with a cosmological constant. The construction of spinor fields in curved spacetime is based on the notions of group theory from Part I and on the local Lorentz invariance. Massless vector fields (massless vector gauge fields) are described and the interactions between scalar, fermion and gauge fields formulated. A detailed discussion of classical conformal transformations and conformal symmetry for both matter fields and vacuum action is also provided.

A CHIRALLY SYMMETRIC EFFECTIVE ACTION FOR VECTOR AND AXIAL VECTOR FIELDS IN A GLOBAL COLOR SYMMETRY MODEL OF QCD

1989 ◽  
Vol 04 (07) ◽  
pp. 1681-1733 ◽  
Author(s):  
C. D. ROBERTS ◽  
J. PRASCHIFKA ◽  
R. T. CAHILL
Keyword(s):  
Effective Action ◽  
Bound States ◽  
Vector Fields ◽  
Axial Vector ◽  
Form Factors ◽  
Local Fields ◽  
Local Action ◽  
Massless Fermion ◽  
Yang Mills ◽  
Local Functions

We consider the quantum field theory of a model of an extended Nambu-Jona-Lasinio type with a QCD based nonlocal fermion current-current interaction which has global SU(Nc) symmetry. We obtain an exact bosonization of this model in four Euclidean dimensions using auxiliary bilocal fields and discuss the dynamical breakdown of chiral symmetry in the massless fermion limit. A local field bosonization is obtained by decomposing the bilocal fields in terms of complete orthonormal sets of functions with the expansion coefficients, which are local functions, identified as the local meson fields. Retaining the ground state pseudoscalar, vector and pseudovector local fields we obtain a local effective action for this sector of the theory. The derivative expansion of the fermionic determinant necessary to obtain this local action is self-regularizing because of the bilocal substructure present in the model which is manifest in the form factors that are associated with the local fields. In our local action the value of each coefficient depends critically on the underlying fermionic dynamics through these form factors and the vacuum functions. As a consequence of this the vector and pseudovector fields in the theory are best interpreted as simple fermion-antifermion bound states rather than as massive Yang-Mills fields or exotic composites of the pseudoscalars; interpretations that we find are not in general admitted when models such as the GCM are treated correctly. Identifying then the physical vector and pseudovector fields with the linearly transforming chiral partners introduced by the bosonization, we obtain an effective action for this sector of the meson spectrum which predicts values for the kinematic and dynamic quantities associated with these fields.

scholarly journals Conformal invariance and the metrication of the fundamental forces

2016 ◽  
Vol 25 (12) ◽  
pp. 1644003 ◽  
Author(s):  
Philip D. Mannheim
Keyword(s):  
String Theory ◽  
Conformal Invariance ◽  
Vector Fields ◽  
Axial Vector ◽  
Gravitational Theory ◽  
Einstein Gravity ◽  
Conformal Gravity ◽  
Yang Mills ◽  
Standard Picture ◽  
Fundamental Forces

We revisit Weyl’s metrication (geometrization) of electromagnetism. We show that by making Weyl’s proposed geometric connection be pure imaginary, not only are we able to metricate electromagnetism, an underlying local conformal invariance makes the geometry be strictly Riemannian and prevents observational gravity from being complex. Via torsion, we achieve an analogous metrication for axial-vector fields. We generalize our procedure to Yang–Mills theories, and achieve a metrication of all the fundamental forces. Only in the gravity sector does our approach differ from the standard picture of fundamental forces, with our approach requiring that standard Einstein gravity be replaced by conformal gravity. We show that quantum conformal gravity is a consistent and unitary quantum gravitational theory, one that, unlike string theory, only requires four spacetime dimensions.

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.

The nature of universal primary interactions of particles

1968 ◽  
Vol 305 (1482) ◽  
pp. 319-343 ◽  
Keyword(s):  
Vector Fields ◽  
Weak Interactions ◽  
Magnetic Moments ◽  
Effective Interaction ◽  
Axial Vector ◽  
Decay Rates ◽  
Coupling Constants ◽  
Strong Interactions ◽  
Electromagnetic Mass ◽  
Strange Particles

A theory of primary interactions between elementary particles is proposed. It is based on the hypothesis that there are three primary interactions: weak, electromagnetic, and strong; and each of them is characterized by a single coupling constant. The primary weak interactions couple the leptons to themselves and to vector and axial vector fields, but not to nucleons. The primary electromagnetic interactions couple the electromagnetic field to the charged leptons or to the neutral vector meson fields, but not to nucleons. The primary strong interactions couple the vector and axial vector fields to the nucleons. All the couplings are universal. On the basis of this theory it is possible to account quantitatively for the anomalous magnetic moments of the nucleons, the ratio of the Gamow –Teller and the Fermi β decay coupling constants, weak magnetism, absence of neutral lepton currents, pion-decay, pion-nucleon scattering lengths, and the principal features of the nuclear force. The theory when extended to strange particles, leads automatically to the suppression of weak decays of strange particles. Our older chirality invariant V – A four-fermion interaction is recovered as the effective interaction for small momentum transfers. No intermediate bosons in the conventional sense are required or expected. The application to the absolute calculation of electromagnetic mass shifts and non-leptonic decay rates yields finite answers which will be discussed in another paper.

GAUGED SU(2)L×SU(2)R/SU(2)L+Rσ MODEL IN THE FRAMEWORK OF NONCOMMUTATIVE GEOMETRY

1994 ◽  
Vol 09 (31) ◽  
pp. 5531-5539 ◽  
Author(s):  
DAE SUNG HWANG ◽  
TAEHOON LEE
Keyword(s):  
Noncommutative Geometry ◽  
Vector Fields ◽  
Axial Vector ◽  
Scalar Fields ◽  
Gauge Fields ◽  
The Matrix ◽  
Vector Gauge ◽  
The Masses ◽  
Higgs Fields ◽  
Matrix Derivative

We study the gauged SU(2) L× SU(2) Rσ model in the SU(2|2) superalgebra formalism. The superconnection is taken to have one-form vector fields as its even part and zero-form scalar fields as its odd part. Incorporating the matrix derivative of noncommutative geometry proposed by Connes and Coquereaux et al., we naturally obtain the spontaneously symmetry broken SU(2) L× SU(2) Rσ model. The masses of the axial vector gauge fields and the Higgs fields are obtained.

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

Gauge anomaly for V-A fields in 4 and 6 dimensional curved space

2017 ◽  
Author(s):  
Satoshi Yajima ◽  
Kohei Eguchi ◽  
Makoto Fukuda ◽  
Tomonori Oka ◽  
Shinji Yamashita
Keyword(s):  
Curved Space ◽  
Gauge Anomaly

scholarly journals The UL(3) × UR(3) Extended Nambu–Jona-Lasinio Model in Differential Regularization

1997 ◽  
Vol 12 (13) ◽  
pp. 2361-2371
Author(s):  
Yaw-Hwang Chen ◽  
Su-Long Nyeo ◽  
Yeou-Wei Yang
Keyword(s):  
Effective Action ◽  
Vector Fields ◽  
Axial Vector ◽  
The One

We employ the method of differential regularization to calculate explicitly the one-loop effective action of a bosonized UL(3) × UR(3) extended Nambu–Jona-Lasinio model consisting of scalar, pseudoscalar, vector and axial vector fields.

DIRAC SEA EFFECTS IN A LINEAR σ MODEL WITH VECTOR AND AXIAL VECTOR FIELDS

1995 ◽  
Vol 10 (07) ◽  
pp. 963-976
Author(s):  
C. A. DE SOUSA
Keyword(s):  
Vector Fields ◽  
Axial Vector ◽  
Collective Phenomena ◽  
Many Body ◽  
New Approach ◽  
Dirac Sea ◽  
Body Techniques ◽  
Classical Vector

We propose a new approach to collective phenomena in a linear σ model which includes classical vector–isovector and pseudovector–isovector fields. The main purpose is to describe meson modes composed of two ingredients: phenomenological structureless fields and [Formula: see text] excitations of the vacuum. This procedure, performed in the context of many-body techniques, provides a natural renormalization process through the [Formula: see text] excitations.

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