The Schrödinger equation in a generalized noncovariant gauge

1990 ◽  
Vol 68 (7-8) ◽  
pp. 579-581 ◽  
Author(s):  
Jamal Nazrul Islam
Keyword(s):  
Functional Equation ◽  
Schrödinger Equation ◽  
Gauge Group ◽  
Schrodinger Equation ◽  
Yang Mills ◽  
Temporal Gauge

The Schrödinger functional equation for the pure Yang–Mills theory with SU(2) as the gauge group is considered in a generalized noncovariant gauge, and related to the Schrödinger equation in the temporal gauge.

scholarly journals RENORMALIZATION OF FUNCTIONAL SCHRÖDINGER EQUATION BY BACKGROUND FIELD METHOD

1998 ◽  
Vol 13 (21) ◽  
pp. 1709-1717 ◽  
Author(s):  
K. ZAREMBO
Keyword(s):  
Renormalization Group ◽  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Background Field ◽  
Field Method ◽  
Asymptotic Freedom ◽  
Yang Mills ◽  
State Wave ◽  
Background Field Method

Renormalization group transformations for Schrödinger equation are performed in both φ4 and Yang–Mills theories. The dependence of the ground state wave functional on rapidly oscillating fields is found. For Yang–Mills theory, this dependence restricts a possible form of variational ansatz compatible with asymptotic freedom.

scholarly journals Note on nonlinear Schrödinger equation, KdV equation and 2D topological Yang–Mills–Higgs theory

2019 ◽  
Vol 34 (15) ◽  
pp. 1950074
Author(s):  
Jun Nian
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Kdv Equation ◽  
Nonlinear Schrodinger Equation ◽  
Yang Mills ◽  
Nonlinear Schrödinger ◽  
Small Coupling ◽  
The Kdv Equation ◽  
The Continuum

In this paper, we discuss the relation between the [Formula: see text]D nonlinear Schrödinger equation and the KdV equation. By applying the boson/vortex duality, we can map the classical nonlinear Schrödinger equation into the classical KdV equation in the small coupling limit, which corresponds to the UV regime of the theory. At quantum level, the two theories satisfy the Bethe ansatz equations of the spin-[Formula: see text] [Formula: see text] chain and the [Formula: see text] chain in the continuum limit, respectively. Combining these relations with the dualities discussed previously in the literature, we propose a duality web in the UV regime among the nonlinear Schrödinger equation, the KdV equation and the 2D [Formula: see text] topological Yang–Mills–Higgs theory.

On Yang-Mills theory in the temporal gauge

1989 ◽  
Vol 421 (1861) ◽  
pp. 279-301 ◽  
Keyword(s):  
Functional Equation ◽  
Wave Function ◽  
Power Series ◽  
Ground State ◽  
Constraint Equation ◽  
Time Dimension ◽  
Yang Mills ◽  
Temporal Gauge ◽  
Vector Bosons ◽  
Three Space

A set of partial differential equations are obtained that are equivalent to the gauge constraint functional equation in the temporal gauge for a set of vector bosons interacting through a Yang-Mills type Lagrangian. This is done by expanding the wave function in a functional power series. The first two orders are solved explicitly for the case of two space and one time dimension. A set of solutions is also presented of the gauge constraint equation to the first two orders for three space and one time dimension. A generalization to 3 + 1 dimensions of a conjecture in 2 + 1 dimensions made by Feynman for the ground state of this problem is examined. It is shown that the conjectured wave function satisfies the gauge constraint and Schrodinger equations to second order in the fields.

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