Superconformal anomalies from the path-integral measure

1986 ◽  
Vol 34 (2) ◽  
pp. 533-535 ◽  
Author(s):  
B. Spence
Keyword(s):  
Path Integral ◽  
Integral Measure

scholarly journals ABELIAN ANOMALIES IN NONLOCAL REGULARIZATION

1994 ◽  
Vol 09 (26) ◽  
pp. 4549-4564 ◽  
Author(s):  
M.A. CLAYTON ◽  
L. DEMOPOULOS ◽  
J.W. MOFFAT
Keyword(s):  
Path Integral ◽  
Invariant Theory ◽  
Axial Anomaly ◽  
Regularization Scheme ◽  
Integral Measure ◽  
Nonlocal Regularization ◽  
Noether Current

The nonlocal regularization of QED is shown to possess an axial anomaly of the same form as other regularization schemes. The Noether current is explicitly constructed and the symmetries are shown to be violated, whereas the identities constructed when one properly considers the contribution from the path integral measure are respected. We also discuss the merits and new features of the regularization scheme, as well as the barrier to quantizing the fully gauged chiral-invariant theory.

PATH INTEGRAL ON THE EXTREME FIELD CONFIGURATIONS

2011 ◽  
Vol 26 (01) ◽  
pp. 135-148
Author(s):  
V. M. KHATSYMOVSKY
Keyword(s):  
Path Integral ◽  
Hamiltonian Path ◽  
Hamiltonian Formalism ◽  
Tangential Component ◽  
Generalized Function ◽  
Time Axis ◽  
Generalized Coordinates ◽  
Fast Change ◽  
Integral Measure ◽  
Gravity System

The canonical Hamiltonian path integral measure obeys certain rule which relates such measure on the paths defined on the whole time axis to the measures on the paths defined on the regions constituting the time axis. We show that this "gluing" rule can be reproduced without referring to Hamiltonian formalism, by substituting field configurations with arbitrarily fast change of the fields at the boundary points of these regions into action and viewing the path integral in the sense of generalized function. Now the coordinate along which gluing proceeds can be not only the time. The piecewise-flat (simplicial) minisuperspace gravity system is considered. Arbitrarily fast change of the (tangential component of) metric between the two 4-simplices with common 3-face is studied. That is, we generalize piecewise-flat anzats by allowing tangential metric to be function of the distance from the 3-face in the neighborhood of this 3-face. The action is nondegenerate (nonsingular) with respect to these additional generalized coordinates. The rule for gluing the path integral measures on separate 4-simplices is found. The resulting general expression covers a large variety of the measures including those usually used in numerical calculations and allows one to specify the measure in some applications.

scholarly journals SPIN-STATISTICS THEOREM IN PATH INTEGRAL FORMULATION

2001 ◽  
Vol 16 (24) ◽  
pp. 4025-4044 ◽  
Author(s):  
KAZUO FUJIKAWA
Keyword(s):  
Path Integral ◽  
Energy Condition ◽  
Integral Formulation ◽  
Positive Energy ◽  
Path Integral Formulation ◽  
Dimensional Theory ◽  
Scalar Particles ◽  
Dirac Particles ◽  
Integral Measure ◽  
Local Path

We present a coherent proof of the spin-statistics theorem in path integral formulation. The local path integral measure and Lorentz-invariant local Lagrangian, when combined with the Green functions defined in terms of time ordered products, ensure causality regardless of statistics. The Feynman m-iε prescription ensures the positive energy condition regardless of statistics, and the abnormal spin-statistics relation for both the spin-0 scalar particles and spin-1/2 Dirac particles is excluded if one imposes the positive norm condition in conjunction with Schwinger's action principle. The minus commutation relation between one Bose and one Fermi field arises naturally in the path integral. The Feynman m-iε prescription also ensures a smooth continuation to Euclidean theory, for which the use of the Weyl anomaly is illustrated to exclude the abnormal statistics for the scalar and Dirac particles not only in four-dimensional theory but also in two-dimensional theory.

Anomalies, instantons and axions

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Standard Model ◽  
Path Integral ◽  
Electric Charge ◽  
Gauge Invariant ◽  
Axial Anomaly ◽  
Yang Mills ◽  
Integral Measure ◽  
The Standard Model ◽  
Electroweak Sector

The axial anomaly is derived both from the non-invariance of the path-integral measure under UA(1) transformations and calculations of specific triangle diagrams. It is demonstrated that the anomalous terms are cancelled in the electroweak sector of the standard model, if the electric charge of all fermions adds up to zero. The CP-odd term F̃μν‎Fμν‎ introduced by the axial anomaly is a gauge-invariant renormalisable interaction which is also generated by instanton transitions between Yang–Mills vacua with different winding numbers. The Peceei–Quinn symmetry is discussed as a possible explanation why this term does not contribute to the QCD action.

scholarly journals On the gauge-invariant path-integral measure for the overlap Weyl fermions in 16 of SO(10)

2019 ◽  
Vol 2019 (11) ◽  
Author(s):  
Yoshio Kikukawa
Keyword(s):  
Path Integral ◽  
Boundary Phase ◽  
Basic Question ◽  
Spinor Representation ◽  
Gauge Invariant ◽  
Fermion Model ◽  
Left Handed ◽  
Integral Measure ◽  
The Right ◽  
Weyl Fermions

Abstract We consider the lattice formulation of SO(10) chiral gauge theory with left-handed Weyl fermions in the 16-dimensional spinor representation ($\underline{16}$) within the framework of the overlap fermion/Ginsparg–Wilson relation. We define a manifestly gauge-invariant path-integral measure for the left-handed Weyl field using all the components of the Dirac field, but the right-handed part of it is just saturated completely by inserting a suitable product of the SO(10)-invariant ’t Hooft vertices in terms of the right-handed field. The definition of the measure applies to all possible topological sectors of admissible link fields. The measure possesses all required transformation properties under lattice symmetries and the induced effective action is CP invariant. The global U(1) symmetry of the left-handed field is anomalous due to the non-trivial transformation of the measure, while that of the right-handed field is explicitly broken by the ’t Hooft vertices. There remains the issue of smoothness and locality in the gauge-field dependence of the Weyl fermion measure, but the question is well defined and the necessary and sufficient condition for this property is formulated in terms of the correlation functions of the right-handed auxiliary fields. In the weak gauge-coupling limit at least, all the auxiliary fields have short-range correlations and the question can be addressed further by Monte Carlo methods without encountering the sign problem. We also discuss the relations of our formulation to other approaches/proposals to decouple the species doubling/mirror degrees of freedom. These include the Eichten–Preskill model, the mirror-fermion model with overlap fermions, the domain-wall fermion model with the boundary Eichten–Preskill term, 4D topological insulator/superconductor with a gapped boundary phase, and the recent studies on the PMS phase/“mass without symmetry breaking”. We clarify the similarities and differences in the technical details and show that our proposal is a unified and well defined testing ground for that basic question.

The regularized phase space path integral measure for a scalar field coupled to gravity

1990 ◽  
Vol 335 (1) ◽  
pp. 166-196 ◽  
Author(s):  
Machiko Hatsuda ◽  
Peter van Nieuwenhuizen ◽  
Walter Troost ◽  
Antoine Van Proeyen
Keyword(s):  
Phase Space ◽  
Scalar Field ◽  
Path Integral ◽  
Integral Measure

Chiral bosonization of superconformal ghosts on the Riemann surface and path-integral measure

1989 ◽  
Vol 227 (1) ◽  
pp. 73-80 ◽  
Author(s):  
Ursula Carow-Watamura ◽  
Zyun F. Ezawa ◽  
Kuni Harada ◽  
Akinori Tezuka ◽  
Satoshi Watamura
Keyword(s):  
Riemann Surface ◽  
Path Integral ◽  
Integral Measure
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