scholarly journals Induced Parity Violation in Odd Dimensions

1994 ◽  
Vol 47 (4) ◽  
pp. 465 ◽  
Author(s):  
R Delbourgo ◽  
AB Waites
Keyword(s):  
Parity Violation ◽  
Mass Term ◽  
Field Theories ◽  
Fermion Mass ◽  
Odd Dimensions

One of the interesting features about field theories in odd dimensions is the induction of parity-violating terms and well-defined finite topological actions via quantum loops if a fermion mass term is originally present and conversely. Aspects of this issue are illustrated for electrodynamics in 2+ 1 and 4+ 1 dimensions.

scholarly journals THE ζ FUNCTION ANSWER TO PARITY VIOLATION IN THREE-DIMENSIONAL GAUGE THEORIES

1996 ◽  
Vol 11 (15) ◽  
pp. 2643-2660 ◽  
Author(s):  
R.E. GAMBOA SARAVÍ ◽  
G.L. ROSSINI ◽  
F.A. SCHAPOSNIK
Keyword(s):  
Gauge Field ◽  
Parity Violation ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Mass Term ◽  
Three Dimensions ◽  
Fermion Mass ◽  
Chern Simons ◽  
Fermion Current ◽  
Arbitrary Gauge

We study parity violation in (2+1)-dimensional gauge theories coupled to massive fermions. Using the ζ function regularization approach we evaluate the ground state fermion current in an arbitrary gauge field background, showing that it gets two different contributions which violate parity invariance and induce a Chern–Simons term in the gauge field effective action. One is related to the well-known classical parity breaking produced by a fermion mass term in three dimensions; the other, already present for massless fermions, is related to peculiarities of gauge-invariant regularization in odd-dimensional spaces.

scholarly journals MAJORANA-LIKE (j, 0) ⊕ (0, j) REPRESENTATION SPACES: CONSTRUCTION AND PHYSICAL INTERPRETATION

1994 ◽  
Vol 09 (05) ◽  
pp. 439-450 ◽  
Author(s):  
D.V. AHLUWALIA ◽  
M.B. JOHNSON ◽  
T. GOLDMAN
Keyword(s):  
Wave Equation ◽  
Physical Interpretation ◽  
Parity Violation ◽  
Arbitrary Spin ◽  
Field Theories ◽  
Quantum Field ◽  
Unified Field Theories ◽  
Physical Content ◽  
Unified Field ◽  
Representation Spaces

We present a formalism that extends the Majorana-construction to arbitrary spin (j, 0) ⊕ (0, j) representation spaces. For the example case of spin-one, a wave equation satisfied by the Majorana-like (1, 0) ⊕ (0, 1) spinors is constructed and its physical content explored. The (j, 0) ⊕ (0, j) Majorana-construct is found to possess an unusual classical and quantum field theoretic structure. Relevance of our formalism to parity violation, hadronic phenomenologies, and grand unified field theories is briefly pointed out.

scholarly journals Composite gravitons from metric-independent quantum field theories

2019 ◽  
Vol 35 (04) ◽  
pp. 2030002
Author(s):  
Christopher D. Carone
Keyword(s):  
Mass Term ◽  
Scalar Fields ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Graviton Mass ◽  
Massless Limit

We review some recent works by Carone, Erlich and Vaman on composite gravitons in metric-independent quantum field theories, with the aim of clarifying a number of basic issues. Focusing on a theory of scalar fields presented previously in the literature, we clarify the meaning of the tunings required to obtain a massless graviton. We argue that this formulation can be interpreted as the massless limit of a theory of massive composite gravitons in which the graviton mass term is not of Pauli–Fierz form. We then suggest closely related theories that can be defined without such a limiting procedure (and hence without worry about possible ghosts). Finally, we comment on the importance of finding a compelling ultraviolet completion for models of this type, and discuss some possibilities.

scholarly journals Testing a non-perturbative mechanism for elementary fermion mass generation: lattice setup

2018 ◽  
Vol 175 ◽  
pp. 08009 ◽  
Author(s):  
Stefano Capitani ◽  
Giulia Maria de Divitiis ◽  
Petros Dimopoulos ◽  
Roberto Frezzotti ◽  
Marco Garofalo ◽  
...  
Keyword(s):  
Mass Term ◽  
Fermion Mass ◽  
Mass Generation ◽  
Complex Scalar ◽  
Abelian Gauge ◽  
Twisted Mass ◽  
Chiral Transformation ◽  
Complex Scalar Field ◽  
Stringent Test ◽  
Field Theoretical Model

In this contribution we lay down a lattice setup that allows for the nonperturbative study of a field theoretical model where a SU(2) fermion doublet, subjected to non-Abelian gauge interactions, is also coupled to a complex scalar field doublet via a Yukawa and an “irrelevant” Wilson-like term. Using naive fermions in quenched approximation and based on the renormalizedWard identities induced by purely fermionic chiral transformations, lattice observables are discussed that enable: a) in theWigner phase, the determinations of the critical Yukawa coupling value where the purely fermionic chiral transformation become a symmetry up to lattice artifacts; b) in the Nambu-Goldstone phase of the resulting critical theory, a stringent test of the actual generation of a fermion mass term of non-perturbative origin. A soft twisted fermion mass term is introduced to circumvent the problem of exceptional configurations, and observables are then calculated in the limit of vanishing twisted mass.

scholarly journals A translational flavor symmetry in the mass terms of Dirac and Majorana fermions

2021 ◽  
Author(s):  
Zhi-zhong Xing
Keyword(s):  
Mass Matrix ◽  
Mass Term ◽  
Fermion Mass ◽  
Unitary Matrix ◽  
Majorana Fermions ◽  
Flavor Symmetry ◽  
Fermion Fields ◽  
Starting Point ◽  
Current Experimental Data ◽  
Charged Leptons

Abstract Requiring the effective mass term for a category of fundamental Dirac or Majorana fermions of the same electric charge to be invariant under the translational transformations $\psi^{}_{\alpha \rm L (R)} \to \psi^{}_{\alpha \rm L (R)} + n^{}_{\alpha} z^{}_{\psi \rm L(R)}$ in the flavor space, where $n^{}_\alpha$ and $z^{}_{\psi \rm L(R)}$ stand respectively for the flavor-dependent complex numbers and a constant spinor field anticommuting with the fermion fields, we show that $n^{}_\alpha$ can be identified as the elements $U^{}_{\alpha i}$ in the $i$-th column of the unitary matrix $U$ used to diagonalize the corresponding Hermitian or symmetric fermion mass matrix $M^{}_\psi$, and $m^{}_i = 0$ holds accordingly. We find that the reverse is also true. Now that the mass spectra of charged leptons, up- and down-type quarks are all strongly hierarchical and current experimental data allow the lightest neutrino to be massless, we argue that the zero mass limit for the first-family fermions and the translational flavor symmetry behind it should be a natural starting point for building viable fermion mass models.

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