Quantum corrections to the geodesic equation

1989 ◽  
Vol 67 (9) ◽  
pp. 837-840 ◽  
Author(s):  
D. G. C. McKeon
Keyword(s):  
Sigma Model ◽  
Equation Of Motion ◽  
Geodesic Equation ◽  
Quantum Corrections ◽  
Explicit Calculation ◽  
Nonlinear Sigma Model ◽  
Model Operator ◽  
One Dimensional ◽  
Loop Expansion ◽  
Background Curvature

The geodesic equation of motion for a particle moving in a background gravitational field can be derived from an action that is essentially that of a one-dimensional bosonic nonlinear sigma model. We quantize the particle, and obtain its effective action to lowest order in both the background curvature and the loop expansion, using the background quantization procedure appropriate to the nonlinear sigma model. Operator regularization is used to regulate the theory. Explicit calculation shows that these lowest order corrections vanish exactly.

scholarly journals METAPLECTIC SPINOR FIELDS AND GLOBAL ANOMALIES

1995 ◽  
Vol 10 (01) ◽  
pp. 65-88 ◽  
Author(s):  
M. REUTER
Keyword(s):  
Phase Space ◽  
Sigma Model ◽  
Target Space ◽  
Spin Manifold ◽  
Nonlinear Sigma Model ◽  
Metaplectic Representation ◽  
One Dimensional ◽  
Path Integral Representation ◽  
Infinite Dimensional ◽  
Spinor Fields

We investigate spinor fields on phase spaces. Under local frame rotations they transform according to the (infinite-dimensional, unitary) metaplectic representation of Sp(2N), which plays a role analogous to the Lorentz group. We introduce a one-dimensional nonlinear sigma model whose target space is the phase space under consideration. The global anomalies of this model are analyzed, and it is shown that its fermionic partition function is anomalous exactly if the underlying phase space is not a spin manifold, i.e. if metaplectic spinor fields cannot be introduced consistently. The sigma model is constructed by giving a path integral representation to the Lie transport of spinors along the Hamiltonian flow.

HUBBARD CHAIN EXTENDED TO INCORPORATE THE PEIERLS INSTABILITY

1992 ◽  
Vol 06 (11) ◽  
pp. 637-647
Author(s):  
ADRIAAN M. J. SCHAKEL
Keyword(s):  
Sigma Model ◽  
Qualitative Difference ◽  
Fundamental Property ◽  
Nonlinear Sigma Model ◽  
One Dimensional ◽  
Long Wavelength ◽  
Peierls Instability ◽  
Two Phases ◽  
The Continuum ◽  
Topological Term

The Hubbard chain is extended so as to incorporate the Peierls instability which is a fundamental property of one-dimensional metals. The resulting theory is analysed in the continuum. In the limit of low-energy and long-wavelength it is described by the O(3) nonlinear sigma model. It is argued that the theory has two phases. In one phase the excitation spectrum is gapless, while in the other phase it has a gap. This qualitative difference between the two states is shown to arise from the fact that in the massless phase the O(3) model acquires a topological term. Besides changing the spectrum of the theory, this term is shown to also change statistics.

scholarly journals N=2 Supersymmetry with Central Charge: A Twofold Implementation

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
L. P. R. Ospedal ◽  
R. C. Terin
Keyword(s):  
Sigma Model ◽  
Central Charge ◽  
Classical Mechanics ◽  
Theoretical Framework ◽  
Two Dimensions ◽  
Nonlinear Sigma Model ◽  
Two Dimensional ◽  
One Dimensional ◽  
Matter Model

In this work, we analyze an extended N=2 supersymmetry with central charge and develop its superspace formulation under two distinct viewpoints. Initially, in the context of classical mechanics, we discuss the introduction of deformed supersymmetric derivatives and their consequence on the deformation of one-dimensional nonlinear sigma model. After that, considering a field-theoretical framework, we present an implementation of this superalgebra in two dimensions, such that one of the coordinates is related to the central charge. As an application, in this two-dimensional scenario, we consider topological (bosonic) configurations of a special self-coupled matter model and present a nontrivial fermionic solution.

scholarly journals CANCELLATION OF UV DIVERGENCES IN THE ${\mathcal N} = 4$ SUSY NONLINEAR SIGMA MODEL IN THREE DIMENSIONS

2001 ◽  
Vol 16 (25) ◽  
pp. 1643-1650 ◽  
Author(s):  
TAKEO INAMI ◽  
YORINORI SAITO ◽  
MASAYOSHI YAMAMOTO
Keyword(s):  
Cotangent Bundle ◽  
Sigma Model ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Target Space ◽  
Quantum Corrections ◽  
Nonlinear Sigma Model ◽  
Leading Order ◽  
Β Function

We study the uv properties of the three-dimensional [Formula: see text] SUSY nonlinear sigma model whose target space is T*(CPN-1) (the cotangent bundle of CPN-1) to higher orders in the 1/N expansion. We calculate the β-function to next-to-leading order and verify that it has no quantum corrections at leading and next-to-leading orders.

scholarly journals Massive gravity from double copy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Arshia Momeni ◽  
Justinas Rumbutis ◽  
Andrew J. Tolley
Keyword(s):  
Sigma Model ◽  
Massive Gravity ◽  
Effective Field ◽  
Effective Theory ◽  
Nonlinear Sigma Model ◽  
Limit Theory ◽  
Four Dimensions ◽  
Yang Mills ◽  
Massive Spin ◽  
Double Copy

Abstract We consider the double copy of massive Yang-Mills theory in four dimensions, whose decoupling limit is a nonlinear sigma model. The latter may be regarded as the leading terms in the low energy effective theory of a heavy Higgs model, in which the Higgs has been integrated out. The obtained double copy effective field theory contains a massive spin-2, massive spin-1 and a massive spin-0 field, and we construct explicitly its interacting Lagrangian up to fourth order in fields. We find that up to this order, the spin-2 self interactions match those of the dRGT massive gravity theory, and that all the interactions are consistent with a Λ3 = (m2MPl)1/3 cutoff. We construct explicitly the Λ3 decoupling limit of this theory and show that it is equivalent to a bi-Galileon extension of the standard Λ3 massive gravity decoupling limit theory. Although it is known that the double copy of a nonlinear sigma model is a special Galileon, the decoupling limit of massive Yang-Mills theory is a more general Galileon theory. This demonstrates that the decoupling limit and double copy procedures do not commute and we clarify why this is the case in terms of the scaling of their kinematic factors.

scholarly journals An emergent universe supported by a nonlinear sigma model

2009 ◽  
Vol 26 (7) ◽  
pp. 075017 ◽  
Author(s):  
A Beesham ◽  
S V Chervon ◽  
S D Maharaj
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Emergent Universe

scholarly journals Isolated skyrmions in the CP2 nonlinear sigma model with a Dzyaloshinskii-Moriya type interaction

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
Yutaka Akagi ◽  
Yuki Amari ◽  
Nobuyuki Sawado ◽  
Yakov Shnir
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Type Interaction
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