Stochastic Quantization of Gauge Fields and Constrained Systems

1986 ◽  
pp. 81-94
Author(s):  
Mikio Namiki
Keyword(s):  
Constrained Systems ◽  
Gauge Fields ◽  
Stochastic Quantization

Geometro-stochastic quantization of gauge fields in curved space-time

1988 ◽  
Vol 100 (6) ◽  
pp. 827-868 ◽  
Author(s):  
E. Prugovečki
Keyword(s):  
Space Time ◽  
Gauge Fields ◽  
Stochastic Quantization ◽  
Curved Space

Ward identities for the stochastic quantization of gauge fields

1988 ◽  
Vol 295 (3) ◽  
pp. 297-331 ◽  
Author(s):  
J. Zinn-Justin ◽  
Daniel Zwanziger
Keyword(s):  
Gauge Fields ◽  
Stochastic Quantization ◽  
Ward Identities

STOCHASTIC QUANTIZATION OF ANTISYMMETRIC TENSOR FIELDS

1986 ◽  
Vol 01 (02) ◽  
pp. 111-118 ◽  
Author(s):  
P.A. AMUNDSSEN ◽  
P.H. DAMGAARD ◽  
B.-S. SKAGERSTAM
Keyword(s):  
Stochastic Process ◽  
Initial Data ◽  
Langevin Equation ◽  
Degrees Of Freedom ◽  
Mass Shell ◽  
Symmetric Tensor ◽  
Gauge Fields ◽  
Stochastic Quantization ◽  
Tensor Fields ◽  
Abelian Gauge

We extend the stochastic quantization procedure of Parisi and Wu to the case of anti-symmetric tensor fields of arbitrary rank. It is shown that the correct number of physical degrees of freedom on mass shell is automatically projected out. The gauge degrees of freedom can be buried in the initial data of the Langevin equation describing the stochastic process in analogy with the treatment of Abelian and non-Abelian gauge fields.

Multiferroics

2017 ◽  
Author(s):  
N. Nagaosa
Keyword(s):  
Spin Structure ◽  
Berry Phase ◽  
Spin Current ◽  
Electric Polarization ◽  
Constrained Systems ◽  
Gauge Fields ◽  
Spin States ◽  
Recent Developments ◽  
Electronic Configurations ◽  
Vector Spin Chirality

This chapter delves into the physics of multiferroics, the recent developments of which are discussed here from the viewpoint of the spin current and “emergent electromagnetism” for constrained systems. It presents the three sources of U(1) gauge fields, namely, the Berry phase associated with the noncollinear spin structure, the spin-orbit interaction (SOI), and the usual electromagnetic field. The chapter reviews multiferroic phenomena in noncollinear magnets from this viewpoint and discusses theories of multiferroic behavior of cycloidal helimagnets in terms of the spin current or vector spin chirality. Relativistic SOI leads to a coupling between the spin current and the electric polarization, and hence the ferroelectric and dielectric responses are a new and important probe for the spin states and their dynamical properties. Microscopic theories of the ground state polarization for various electronic configurations, collective modes including the electromagnon, and some predictions including photoinduced chirality switching are discussed with comparison to experimental results.

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