BRST-QUANTIZATION OF BOSONIC STRINGS AND HYPERTWISTORS

1990 ◽  
Vol 05 (25) ◽  
pp. 2057-2062 ◽  
Author(s):  
A. D. POPOV
Keyword(s):  
Phase Space ◽  
Bosonic Strings ◽  
Fock Space ◽  
Brst Quantization ◽  
Geometric Quantization ◽  
Bosonic String ◽  
Total Space ◽  
Complex Structures ◽  
Brst Invariance

We consider the relation between geometric quantization of bosonic strings and the Becchi-Rouet-Stora-Tyutin (BRST) approach. We introduce the space of hypertwistors as the total space of the bundle of complex structures over the phase space of bosonic string. The conditions of the BRST invariance, determining the Fock space of the bosonic string, have been formulated in terms of the ghost bundle over the hypertwistor space.

EQUIVALENCE OF THE LAGRANGIAN AND HAMILTONIAN BRST CHARGES FOR THE BOSONIC STRING IN THE HARMONIC AND CONFORMAL GAUGES

1988 ◽  
Vol 03 (05) ◽  
pp. 1081-1101 ◽  
Author(s):  
V. DEL DUCA ◽  
L. MAGNEA ◽  
P. VAN NIEUWENHUIZEN
Keyword(s):  
Phase Space ◽  
Equations Of Motion ◽  
Hamiltonian Formulation ◽  
Point Of View ◽  
Bosonic String ◽  
Lagrangian Formalism ◽  
Brst Charge ◽  
Gauge Fixing ◽  
Conformal Gauge ◽  
Brst Invariance

We consider the BRST formalism for the bosonic string in arbitrary gauges, both from the Hamiltonian and from the Lagrangian point of view. In the Hamiltonian formulation we construct the BRST charge Q(H) following the Batalin-Fradkin-Fradkina-Vilkovisky (BFFV) formalism in phase space. In the Lagrangian formalism, we use the Noether procedure to construct the BRST charge Q(L) in configuration space. We then discuss how to go from configuration to phase space and demonstrate that the dependence of Q(L) on the gauge fixing disappears and that both charges become equal. We work through two gauges in detail: the conformal gauge and the de Donder (harmonic) gauge. In the conformal gauge one must use equations of motion, and a simple canonical transformation is found which exhibits the equivalence. In the de Donder gauge, nontrivial canonical transformations are needed. Our results overlap with work by Beaulieu, Siegel and Zwiebach on the de Donder gauge, but since we only require BRST invariance and not anti-BRST invariance, we need simpler field redefinitions; moreover, we stay off-shell.

UNDERSTANDING FUJIKAWA REGULATORS FROM PAULI-VILLARS REGULARIZATION OF GHOST LOOPS

1989 ◽  
Vol 04 (15) ◽  
pp. 3959-3982 ◽  
Author(s):  
A. DIAZ ◽  
W. TROOST ◽  
P. VAN NIEUWENHUIZEN ◽  
A. Van PROEYEN
Keyword(s):  
Gravitational Field ◽  
Bosonic String ◽  
Ghost Number ◽  
Two Dimensional ◽  
Mass Terms ◽  
Brst Invariance ◽  
Villars Regularization

We construct mass terms for the ghost and antighost in the bosonic string which preserve coordinate BRST invariance. This allows us to compute the Weyl and ghost number anomalies with Pauli-Villars regularization. An algorithm is derived for the construction of those regulators in the Fujikawa scheme which yield consistent anomalies. In the formulation with the BRST auxiliary fields we find that the nonpropagating two-dimensional gravitational field must be regulated in the same way as the antighost. It contributes the same amount to the anomaly as the antighosts do when one eliminates the auxiliary fields.

STRING EQUATIONS OF MOTION FROM VANISHING CURVATURE

1991 ◽  
Vol 06 (08) ◽  
pp. 1319-1333 ◽  
Author(s):  
MARK J. BOWICK ◽  
KONG-QING YANG
Keyword(s):  
Vector Bundles ◽  
Adiabatic Approximation ◽  
Equations Of Motion ◽  
Bosonic String ◽  
Complex Structures ◽  
Closed Bosonic String

The equations of motion for the massless modes of the closed bosonic string are obtained in the adiabatic approximation from the requirement of the vanishing of the curvature of appropriate vector bundles over the space of complex structures Diff S1/S1. This vanishing is required for physical states to be independent of string parametrization.

scholarly journals BRST Quantization of the Proca Model Based on the BFT and the BFV Formalism

1997 ◽  
Vol 12 (23) ◽  
pp. 4217-4239 ◽  
Author(s):  
Yong-Wan Kim ◽  
Mu-In Park ◽  
Young-Jai Park ◽  
Sean J. Yoon
Keyword(s):  
Phase Space ◽  
Brst Quantization ◽  
Brst Symmetry ◽  
Mass Term ◽  
Class Constraint ◽  
Extended Phase ◽  
Breaking Effect ◽  
Linear Character ◽  
Constraint System ◽  
Gauge Fixing

The BRST quantization of the Abelian Proca model is performed using the Batalin–Fradkin–Tyutin and the Batalin-Fradkin-Vilkovisky formalism. First, the BFT Hamiltonian method is applied in order to systematically convert a second class constraint system of the model into an effectively first class one by introducing new fields. In finding the involutive Hamiltonian we adopt a new approach which is simpler than the usual one. We also show that in our model the Dirac brackets of the phase space variables in the original second class constraint system are exactly the same as the Poisson brackets of the corresponding modified fields in the extended phase space due to the linear character of the constraints comparing the Dirac or Faddeev–Jackiw formalisms. Then, according to the BFV formalism we obtain that the desired resulting Lagrangian preserving BRST symmetry in the standard local gauge fixing procedure naturally includes the Stückelberg scalar related to the explicit gauge symmetry breaking effect due to the presence of the mass term. We also analyze the nonstandard nonlocal gauge fixing procedure.

scholarly journals BRST QUANTIZATION OF SU(2/1) ELECTROWEAK THEORY IN THE SUPERCONNECTION APPROACH, AND THE HIGGS MESON MASS

1996 ◽  
Vol 11 (19) ◽  
pp. 3509-3522 ◽  
Author(s):  
DAE SUNG HWANG ◽  
CHANG-YEONG LEE ◽  
YUVAL NE’EMAN
Keyword(s):  
Renormalization Group ◽  
Top Quark ◽  
Brst Quantization ◽  
Higgs Field ◽  
Mass Term ◽  
Scalar Fields ◽  
Meson Mass ◽  
Electroweak Theory ◽  
Renormalization Group Equations ◽  
Brst Invariance

A superconnection, in which a scalar field enters as a zero-form in the odd part of the superalgebra, is used in the BRST quantization of the SU (2/1) “internally superunified” electroweak theory. A quantum action is obtained, by applying symmetric BRST/anti-BRST invariance. Evaluating the mass of the Higgs field, we exhibit the consistency between two approaches: (a) applying the supergroup’s (gauge) value for λ, the coupling of the scalar field’s quartic potential, to the conventional (spontaneous symmetry breakdown) evaluation; (b) dealing with the superconnection components as a supermultiplet of an (global) internal supersymmetry. This result thus provides a general foundation for the use of “internal” supergauges. With SU (2/1) broken by the negative squared mass term for the Higgs field and with the matter supermultiplets involving added “effective” ghost states, there is no reason to expect the symmetry’s couplings not to be renormalized. This explains the small difference between predicted and measured values for sin2θw, namely the other coupling fixed by SU (2/1) beyond the Standard Model’s SU(2)×U(1), and where the experimental results are very precise. Using the renormalization group equations and those experimental data, we thus evaluate the energy E8 at which the SU (2/1) predicted value of 0.25 is expected to correspond to the experimental values. With SU (2/1) precise at that energy Es=5 TeV , we then apply the renormalization group equations again, this time to evaluate the corrections to the above λ, the quartic coupling of the scalar fields; as a result we obtain corrections to the prediction for the Higgs meson’s mass. Our result predicts the Higgs’ mass [170 GeV, according to unrenormalized SU (2/1)] to be as low as 130±6 GeV , using for the top quark mass the recently measured value of 174 GeV .

scholarly journals Proposal of a Computational Approach for Simulating Thermal Bosonic Fields in Phase Space

Physics ◽  
2019 ◽  
Vol 1 (3) ◽  
pp. 402-411 ◽  
Author(s):  
Alessandro Sergi ◽  
Roberto Grimaudo ◽  
Gabriel Hanna ◽  
Antonino Messina
Keyword(s):  
Phase Space ◽  
Thermal Noise ◽  
Fock Space ◽  
Vacuum State ◽  
Thermal Bath ◽  
Wigner Transform ◽  
Thermal Vacuum ◽  
Thermo Field Dynamics ◽  
Augmented Space ◽  
Thermal Vacuum State

When a quantum field is in contact with a thermal bath, the vacuum state of the field may be generalized to a thermal vacuum state, which takes into account the thermal noise. In thermo field dynamics, this is realized by doubling the dimensionality of the Fock space of the system. Interestingly, the representation of thermal noise by means of an augmented space is also found in a distinctly different approach based on the Wigner transform of both the field operators and density matrix, which we pursue here. Specifically, the thermal noise is introduced by augmenting the classical-like Wigner phase space by means of Nosé–Hoover chain thermostats, which can be readily simulated on a computer. In this paper, we illustrate how this may be achieved and discuss how non-equilibrium quantum thermal distributions of the field modes can be numerically simulated.

scholarly journals BRST INVARIANCE OF NONLOCAL CHARGES AND MONODROMY MATRIX OF BOSONIC STRING ON AdS5×S5

2007 ◽  
Vol 22 (12) ◽  
pp. 2239-2263 ◽  
Author(s):  
J. KLUSOŇ
Keyword(s):  
Monodromy Matrix ◽  
Bosonic String ◽  
Chiral Model ◽  
Hamiltonian Method ◽  
Principal Chiral Model ◽  
Brst Invariance

Using the generalized Hamiltonian method of Batalin, Fradkin and Vilkovsky we develop the BRST formalism for the bosonic string on AdS 5× S 5 formulated as principal chiral model. Then we show that the monodromy matrix and nonlocal charges are BRST invariant.

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