EQUIVALENCE OF LAGRANGIAN AND HAMILTONIAN BRST FORMALISM IN GAUGE FIELD CASE
The gauge field is a constrained system where the Noether charge generates gauge symmetry. The gauge field is quantized through canonical and paths integral quantization which give the physical properties of the indeterministic system. From the Faddeev-Popov method applied in path integral quantizat...
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| Format: | Final Project |
| Language: | Indonesia |
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| Online Access: | https://digilib.itb.ac.id/gdl/view/41483 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | The gauge field is a constrained system where the Noether charge generates gauge symmetry. The gauge field is quantized through canonical and paths integral quantization which give the physical properties of the indeterministic system. From the Faddeev-Popov method applied in path integral quantization gives the existence of a ghost field. Ghost field can also be obtained through the least action principle and gave birth to the concept of BRST symmetry which extends gauge symmetry. BRST symmetry can also be derived by extending the Poisson brackets/ commutation relations to the ghost field and applying the nilpotent properties to the Noether charge. In the influence of BRST symmetry, the Lagrangian and the Hamiltonian formalism of gauge field are shown to be equivalent through the similarity of the Noether charge properties of both formalism and the validity of the Legendre transformation. In addition, the two formalisms can be expressed in the formalism of Batalin-Vilkovisky (BV)/field-antifield formalism. In addition to the gauge field, BRST symmetry can also be applied to relativistic particles, chiral gauge theory in (1+1) dimensions and relativistic strings. |
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