Author(s):
Suresh C. Jaryal†, Nidhi Mankotia, Abhisek Mohapatra, Soumyaranjan Dash, Ayan Chatterjee
Email(s):
nidhimankotia2000@gmail.com , ayan.theory@gmail.com , suresh.fifthd@gmail.com
Address:
Suresh C. Jaryal†1,2, Nidhi Mankotia‡§1, Abhisek Mohapatra¶, Soumyaranjan Dash‖1, Ayan Chatterjee∗1
1Department of Physics and Astronomical Science, Central University of Himachal Pradesh, Dharamshala- 176215, India.
2Department of Physics and Astronomical Sciences, Central University of Jammu, Samba, J&K- 181143, India.
*Corresponding Author
Published In:
Conference Proceeding, Mathematics in Space and Applied Sciences (ICMSAS-2023)
Year of Publication:
March, 2023
Online since:
March 04, 2023
DOI:
Quantization
of gauge anomaly free Kalb-Ramond Field
Suresh
C. Jaryal1,2, Nidhi Mankotia1, Abhisek Mohapatra¶,
Soumyaranjan Dash1,
Ayan Chatterjee∗1
1Department
of Physics and Astronomical Science, Central University of Himachal Pradesh,
Dharamshala- 176215, India.
2Department
of Physics and Astronomical Sciences, Central University of Jammu, Samba,
J&K- 181143, India.
*Corresponding
Author E-mail: nidhimankotia2000@gmail.com,
ayan.theory@gmail.com, suresh.fifthd@gmail.com
ABSTRACT:
Gauge
theories have constraints among their dynamical variables, and transition from
Lagrangian to Hamiltonian formalism in these theories need special care. With
the help of the Dirac method of constraint systems, we study the gauge anomaly
free Kalb-Ramond field Hµνλ by classifying these constraints in
accordance to the Dirac method. The first class constraints are shown to
generate the appropriate gauge transformations for the field potential Bµν,
given by δBµν = ∂[µλν]. We construct the
reduced phase space and show that the Dirac brackets give the fundamental
brackets for field quantisation.
KEYWORDS:
Quantization,
gauge anomaly free Kalb-Ramond Field.
INTRODUCTION:
Gauge
theories are the basic building blocks of the standard model of elementary
particles [1]. However, many gauge fields, including the higher form fields are
absent from this Standard model. These higher form fields arise naturally in
the field approximations of string theory. For example, the Kalb-Ramond field
finds use in describing the modes of a closed string [2]. On the other hand,
its Hodge dual is the axion, which is considered to be a good candidate for the
dark matter. So, it is appropriate that we try to construct a quantisation of
this Kalb-Ramond field using the Hamiltonian methods [4,5,6].
The
free Kalb-Ramond field was quantised in [3]. We shall however quantise a
modification of this theory, by adding appropriate U(1) fields which make the
field anomaly free [2].
Emergence of secondary constraints:
The
modified theory has Lagrangian density as
REFERENCES:
1.
Peskin, Michael E. and Daniel V. Schroeder, “An introduction to quantum field theory”,
CRC press (2018)
2.
Michel B Green, John h Schwarz, Edward
Witten, “Superstring Theory, Vol. 2”, Cambridge University Press (1988)
3.
R. Kaul, “Quantization of free field
theory of massless anti-symmetric tensor gauge fields of second rank”, Physical
Review D(1978). Vol. 18, no 4, p1127.
4.
P. A. M. Dirac, “Lectures on Quantum
Mechanics”, Dover Publications ( 1964)
5.
Henneaux M. and Teitelboim C., “Quantization
of Gauge Systems”, Princeton University Press (1994)
6.
Sundermeyer, K., “Constrained dynamics
with applications to Yang-Mills theory, general relativity, classical spin,
dual string model”, Germany: Springer (1982)