Topological charge in 1+1 dimensional lattice {phi}{sup 4} theory
Abstract
We investigate the topological charge in 1+1 dimensional {phi}{sup 4} theory on a lattice with antiperiodic boundary condition (APBC) in the spatial direction. We propose a simple order parameter for the lattice theory with APBC and we demonstrate its effectiveness. Our study suggests that kink condensation is a possible mechanism for the orderdisorder phase transition in the 1+1 dimensional {phi}{sup 4} theory. With renormalizations performed on the lattice with periodic boundary condition (PBC), the topological charge in the renormalized theory is given as the ratio of the order parameters in the lattices with APBC and PBC. We present a comparison of topological charges in the bare and the renormalized theory and demonstrate invariance of the charge of the renormalized theory in the broken symmetry phase.
 Authors:
 Theory Group, Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata 700064 (India)
 Publication Date:
 OSTI Identifier:
 20713852
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. D, Particles Fields; Journal Volume: 72; Journal Issue: 9; Other Information: DOI: 10.1103/PhysRevD.72.094504; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BOUNDARY CONDITIONS; COMPARATIVE EVALUATIONS; LATTICE FIELD THEORY; ONEDIMENSIONAL CALCULATIONS; ORDER PARAMETERS; PERIODICITY; PHASE TRANSFORMATIONS; PHI4FIELD THEORY; RENORMALIZATION; SYMMETRY BREAKING; TOPOLOGY
Citation Formats
De, Asit K., Harindranath, A., Maiti, Jyotirmoy, and Sinha, Tilak. Topological charge in 1+1 dimensional lattice {phi}{sup 4} theory. United States: N. p., 2005.
Web. doi:10.1103/PhysRevD.72.094504.
De, Asit K., Harindranath, A., Maiti, Jyotirmoy, & Sinha, Tilak. Topological charge in 1+1 dimensional lattice {phi}{sup 4} theory. United States. doi:10.1103/PhysRevD.72.094504.
De, Asit K., Harindranath, A., Maiti, Jyotirmoy, and Sinha, Tilak. Tue .
"Topological charge in 1+1 dimensional lattice {phi}{sup 4} theory". United States.
doi:10.1103/PhysRevD.72.094504.
@article{osti_20713852,
title = {Topological charge in 1+1 dimensional lattice {phi}{sup 4} theory},
author = {De, Asit K. and Harindranath, A. and Maiti, Jyotirmoy and Sinha, Tilak},
abstractNote = {We investigate the topological charge in 1+1 dimensional {phi}{sup 4} theory on a lattice with antiperiodic boundary condition (APBC) in the spatial direction. We propose a simple order parameter for the lattice theory with APBC and we demonstrate its effectiveness. Our study suggests that kink condensation is a possible mechanism for the orderdisorder phase transition in the 1+1 dimensional {phi}{sup 4} theory. With renormalizations performed on the lattice with periodic boundary condition (PBC), the topological charge in the renormalized theory is given as the ratio of the order parameters in the lattices with APBC and PBC. We present a comparison of topological charges in the bare and the renormalized theory and demonstrate invariance of the charge of the renormalized theory in the broken symmetry phase.},
doi = {10.1103/PhysRevD.72.094504},
journal = {Physical Review. D, Particles Fields},
number = 9,
volume = 72,
place = {United States},
year = {Tue Nov 01 00:00:00 EST 2005},
month = {Tue Nov 01 00:00:00 EST 2005}
}

In this work we perform a detailed numerical analysis of (1+1) dimensional lattice {phi}{sup 4} theory. We explore the phase diagram of the theory with two different parametrizations. We find that symmetry breaking occurs only with a negative masssquared term in the Hamiltonian. The renormalized mass m{sub R} and the field renormalization constant Z are calculated from both coordinate space and momentum space propagators in the broken symmetry phase. The critical coupling for the phase transition and the critical exponents associated with m{sub R}, Z and the order parameter are extracted using a finitesize scaling analysis of the data formore »

Renormalization group study of the soliton mass in the (1+1)dimensional [lambda][Phi][sup 4] lattice model
We compute, in the (1+1)dimensional [lambda][Phi][sup 4] model on the lattice, the soliton mass by means of two very different numerical methods. First, we make use of a creation operator'' formalism, measuring the decay of a certain correlation function. Second, we measure the shift of the vacuum energy between the symmetric and the antiperiodic systems. The obtained results are fully compatible. We compute the continuum limit of the mass from the perturbative renormalization group equations. Special attention is paid to ensure that we are working in the scaling region, where physical quantities remain unchanged along any renormalization group trajectory. Wemore » 
Spontaneous symmetry breaking of (1+1)dimensional [phi][sup 4] theory in lightfront field theory
We study spontaneous symmetry breaking in (1+1)dimensional [phi][sup 4] theory using the lightfront formulation of field theory. Since the physical vacuum is always the same as the perturbative vacuum in lightfront field theory the fields must develop a vacuum expectation value through the zeromode components of the field. We solve the nonlinear operator equation for the zero mode in the onemode approximation. We find that spontaneous symmetry breaking occurs at [lambda][sub critical]=4[pi](3+ [radical]3 )[mu][sup 2], which is consistent with the value [lambda][sub critical]=54.27[mu][sup 2] obtained in the equaltime theory. We calculate the vacuum expectation value as a function of themore » 
Spontaneous symmetry breaking of (1+1)dimensional [phi][sup 4] theory in lightfront field theory. III
We investigate (1+1)dimensional [phi][sup 4] field theory in the symmetric and broken phases using discrete lightfront quantization. We calculate the perturbative solution of the zeromode constraint equation for both the symmetric and broken phases and show that standard renormalization of the theory yields finite results. We study the perturbative zeromode contribution to two diagrams and show that the lightfront formulation gives the same result as the equaltime formulation. In the broken phase of the theory, we obtain the nonperturbative solutions of the constraint equation and confirm our previous speculation that the critical coupling is logarithmically divergent. We discuss the renormalizationmore » 
Spontaneous symmetry breaking of (1+1)dimensional [phi][sup 4] theory in lightfront field theory. II
We discuss spontaneous symmetry breaking of (1+1)dimensional [phi][sup 4] theory in lightfront field theory using a TammDancoff truncation. We show that, even though lightfront field theory has a simple vacuum state which is an eigenstate of the full Hamiltonian, the field can develop a nonzero vacuum expectation value. This occurs because the zero mode of the field must satisfy an operatorvalued constraint equation. In the context of (1+1)dimensional [phi][sup 4] theory we present solutions to the constraint equation using a TammDancoff truncation to a finite number of particles and modes. We study the behavior of the zero mode as amore »