Hamiltonian, path integral and BRST formulations of the Chern–Simons–Higgs theory in the broken symmetry phase

Abstract

The Hamiltonian, path integral and BRST formulations of the Chern-Simons-Higgs theory in two-space one-time dimensions are investigated under appropriate gauge-fixing conditions, in the broken (or frozen) symmetry phase, where the phase ϕ (x µ ) of the complex matter field (x µ ) carries the charge degree of freedom of the complex matter field and is, in fact, akin to the Goldstone boson.

Light-Front Quantization of Chern-Simons-Higgs Theory in the Symmetry Phase

“…Very recently we have studied the instant-form (IF) quantization (IFQ) [15] of this theory in the presence of the Higgs potential on the hyperplanes: x 0 = t = constant, in the so-called symmetry phase (SP) of the Higgs potential [15]. The IFQ of this theory has also been studied by us [16] in the so-called broken (or frozen) symmetry phase of the Higgs potential [14,15,16,17]. In this talk [18], I would consider the Hamiltonian [19,20], path integral [21,22] and BRST [23,24,25] formulations of this theory using the light-front (LF) dynamics [26,27](on the hyperplanes defined by the LC time: (τ ≡ x + = (x 0 +x 1 ) √ 2 = constant) [26,27] in the symmetry phase of the Higgs potential.…”

“…Also, different aspects of this theory have been studied by several authors in various contexts [1]- [18]. We first consider the LF [26,27] Hamiltonian and path integral formulations of this theory (in the so-called symmetry phase of the Higgs potential) [16] under appropriate gaugefixing. The Chern-Simons-Higgs theory in two-space one-time dimensions is defined by the action [1]- [18]:…”

“…In the path integral formulation, the transition to quantum theory is made by writing the vacuum to vacuum transition amplitude for the theory called the generating functional Z[J k ] of the theory [16,17,18,21,22] under the gauge-fixing under consideration, in the presence of the external sources J k as:…”

Light-Front Quantization of the Chern–Simons–Higgs Theory in the Broken Symmetry Phase

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Two-space one-time dimensional Chern-Simons-Higgs theory is quantized on the light-front in the broken (frozen) symmetry phase of the Higgs potential.Gauge theories in two-space one-time dimensions involving Chern-Simons (CS) term coupled to matter fields describe excitations with fractional statistics [1][2][3][4][5][6][7][8]. Such studies form a broad field of study [1][2][3][4][5][6][7][8].

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“…In the following, we study this theory in the so-called broken (or frozen) symmetry phase (BSP) [4,6], of the complex matter field [≡ (x μ )]. For this purpose, for the complex matter field we take [4,7]: …”