Journal
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
Volume 55, Issue 6, Pages 2857-2869Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10773-016-2917-y
Keywords
2D free Abelian 1-form gauge theory; Symmetry principles; Continuous internal symmetries; Canonical (anti)commutators; Creation and annihilation operators; Conserved charges as generators; Hodge theory
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Funding
- CSIR
- UGC, New Delhi, Government of India
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We deduce the canonical brackets for a two (1+1)-dimensional (2D) free Abelian 1-form gauge theory by exploiting the beauty and strength of the continuous symmetries of a Becchi-Rouet-Stora-Tyutin (BRST) invariant Lagrangian density that respects, in totality, six continuous symmetries. These symmetries entail upon this model to become a field theoretic example of Hodge theory. Taken together, these symmetries enforce the existence of exactly the same canonical brackets amongst the creation and annihilation operators that are found to exist within the standard canonical quantization scheme. These creation and annihilation operators appear in the normal mode expansion of the basic fields of this theory. In other words, we provide an alternative to the canonical method of quantization for our present model of Hodge theory where the continuous internal symmetries play a decisive role. We conjecture that our method of quantization is valid for a class of field theories that are tractable physical examples for the Hodge theory. This statement is true in any arbitrary dimension of spacetime.
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