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light-cone Coordinate System in General Relativity

Journal of High Energy Physics, Gravitation and Cosmology 2022年第2期8卷 269-284页

作者： Yingqiu Gu School of Mathematical Science Fudan University Shanghai China

If there exists a null gradient field in 3 + 1 dimensional space-time, we can set up a kind of light-cone coordinate system in the space-time. In such coordinate system, the metric takes a simple form, which is helpful for simplifying and solving the Einstein’s field equation. This light-cone coordinate system has wonderful properties and has been used widely in astrophysics to calculate parameters. We discuss the structure of space-time with light-cone coordinate system in detail. We show how to construct the light-cone coordinate system and obtain the conditions of its existence, and then explain their geometrical and physical meanings.

关键词： light-cone Null Gradient Field Coordinate Transformation Geodesic Einstein’s Field Equation

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light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons Theory under Appropriate Gauge-Fixing

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Journal of Modern Physics 2010年第6期1卷 385-392页

作者： Usha Kulshreshtha Daya Shankar Kulshreshtha James P. Vary 不详

The Chern-Simons theory in two-space one-time dimensions is quantized on the light-front under appropriate gauge-fixing conditions using the Hamiltonian, path integral and BRST formulations.

关键词： Hamiltonian Quantization Path Integral Quantization BRST Quantization Chern-Simons Theories light-cone Quantization light-Front Quantization Constrained Dynamics Quantum Electrodynamics Models in Lower Dimensions

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light-Front Hamiltonian and Path Integral Formulations of the Conformally Gauge-Fixed Polyakov D1 Brane Action with a Scalar Dilation Field

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Journal of Modern Physics 2011年第5期2卷 826-833页

作者： Usha Kulshreshtha Daya Shankar Kulshreshtha 不详

Recently we have studied the instant-form quantization (IFQ) of the conformally gauge-fixed Polyakov D1 brane action with and without a scalar dilaton field using the Hamiltonian and path integral formulations in the equal world-sheet time framework on the hyperplanes defined by the world- sheet time σ0=τ=constant . The light-front quantization (LFQ) of this theory without a scalar dilaton field has also been studied by us recently. In the present work we study the LFQ of this theory in the equal light-cone world-sheet time framework, on the hyperplanes of the light-front defined by the light-cone world-sheet time σ+=τ+σ=constant , using the Hamiltonian and path integral formulations. The light-front theory is seen to be a constrained system in the sense of Dirac. The light-front theory is seen to possess a set of twenty seven primary second-class contraints. In the present work Hamiltonian and path integral quantizations of this theory are studied on the light-front.

关键词： light-Front Quantization Hamiltonian Quantization Path Integral Quantization Constrained Dynamics Constraint Quantization Gauge Symmetry String Gauge Symmetry String Theory D-brane Actions Polyakov Action light-cone Quantization

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String Gauge Symmetries in the Conformally Gauge-Fixed Polyakov D1 Brane Action in the Presence of Background Gauge Fields

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Journal of Modern Physics 2012年第1期3卷 110-115页

作者： Usha Kulshreshtha Daya Shankar Kulshreshtha 不详

Recently we have studied the instant-form quantization (IFQ) and the light-front quantization (LFQ) of the conformally gauge-fixed Polyakov D1 brane action using the Hamiltonian and path integral formulations. The IFQ is studied in the equal world-sheet time framework on the hyperplanes defined by the world- sheet time σ0 = τ = constant and the LFQ in the equal light-cone world-sheet time framework, on the hyperplanes of the light-front defined by the light-cone world-sheet time . The light-front theory is seen to be a constrained system in the sense of Dirac in contrast to the instant-form theory. However, owing to the gauge anomalous nature of these theories, both of these theories are seen to lack the usual string gauge symmetries defined by the world-sheet reparametrization invariance (WSRI) and the Weyl invariance (WI). In the present work we show that these theories when considered in the presence of background gauge fields such as the NSNS 2-form gauge field or in the presence of gauge field and the constant scalar axion field , then they are seen to possess the usual string gauge symmetries (WSRI and WI). In fact, these background gauge fields are seen to behave as the Wess-Zumino/Stueckelberg fields and the terms containing these fields are seen to behave as Wess-Zumino or Stueckelberg terms for these theories.

关键词： light-Front Quantization Hamiltonian Quantization Path Integral Quantization Constrained Dynamics Constraint Quantization Gauge Symmetry String Gauge Symmetry String Theory D-Brane Actions Polyakov Action light-cone Quantization

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