scholarly journals The Schrödinger representation and its relation to the holomorphic representation in linear and affine field theory

2012 ◽  
Vol 53 (7) ◽  
pp. 072301 ◽  
Author(s):  
Robert Oeckl
Keyword(s):  
Field Theory ◽  
Schrödinger Representation ◽  
Holomorphic Representation

CRITICAL BEHAVIOR FROM SCHRÖDINGER REPRESENTATION

1992 ◽  
Vol 07 (22) ◽  
pp. 1975-1981 ◽  
Author(s):  
P. SURANYI
Keyword(s):  
Field Theory ◽  
Ising Model ◽  
Integral Equations ◽  
Critical Behavior ◽  
Transcendental Equation ◽  
Schrödinger Representation ◽  
Correlation Exponent ◽  
Truncation Scheme ◽  
Infinite Set ◽  
Good Agreement

The Schrödinger equation for Φ4 field theory is reduced to an infinite set of integral equations. A systematic truncation scheme is proposed and it is solved in second order to obtain the approximate critical behavior of the renormalized mass. The correlation exponent is given as a solution of a transcendental equation. It is in good agreement with the Ising model in all physical dimensions.

scholarly journals EQUIVALENCE BETWEEN DIFFERENT CLASSICAL TREATMENTS OF THE O(N) NONLINEAR SIGMA MODEL AND THEIR FUNCTIONAL SCHRÖDINGER EQUATIONS

2003 ◽  
Vol 18 (05) ◽  
pp. 755-766 ◽  
Author(s):  
A. A. DERIGLAZOV ◽  
W. OLIVEIRA ◽  
G. OLIVEIRA-NETO
Keyword(s):  
Field Theory ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Sigma Model ◽  
Hamiltonian Formalism ◽  
Original Version ◽  
Nonlinear Sigma Model ◽  
Schrödinger Equations ◽  
Schrödinger Representation ◽  
The Way

In this work we derive the Hamiltonian formalism of the O(N) nonlinear sigma model in its original version as a second-class constrained field theory and then as a first-class constrained field theory. We treat the model as a second-class constrained field theory by two different methods: the unconstrained and the Dirac second-class formalisms. We show that the Hamiltonians for all these versions of the model are equivalent. Then, for a particular factor-ordering choice, we write the functional Schrödinger equation for each derived Hamiltonian. We show that they are all identical which justifies our factor-ordering choice and opens the way for a future quantization of the model via the functional Schrödinger representation.

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