Calculation of higher mass-dimensional effective Lagrangians in quantum field theory
Date of Publication
2003
Document Type
Master's Thesis
Degree Name
Master of Science in Physics
College
College of Science
Department/Unit
Physics
Thesis Adviser
Emmanuel T. Rodulfo
Defense Panel Chair
Ermys B. Bornilla
Defense Panel Member
Reuben V. Quiroga
Jose Perico H. Esguerra
Abstract/Summary
A prescription for calculating low-energy one-loop higher-mass dimensional effective Lagrangians for non-Abelian field theories is constructed in the spirit of quasilocal background field method. Basis of Lorentz and gauge-invariant monomials of similar mass-dimensions acting as building blocks are matrix-multiplied in a specified order (usually dictated by a permutation of tensorial indices) generating the much needed invariants. The same set of building blocks is used to generate higher-order corrections for a specific mass-dimension. Though the gauge group, the spacetime dimensions, the order of corrections that can be included and the mass-dimensions that can be formed are all kept arbitrary in the prescription, we constructed basis invariants from 3 up to 12 mass-dimensions to accommodate higher-order corrections up to fourth-order. With these basis, we pursued solving the zeroth-order corrections leading to invariants from 2 up to 16 mass-dimensions, for first-order from 4 up to 8 mass-dimensions, second and third order corrections from 6 up to 8 mass-dimensions. As a result, we have reproduced the zeroth-order corrections showing dependence on the covariant derivative of the background matrix potential. Previous calculation was done up to 12 mass-dimensions but this dependence was not shown in closed form. For higher-order corrections, the case for 4 up to 6 mass-dimensions are also reproduced. Finally, we calculated the case for 8 mass-dimensions which is reduced only by exploiting the antisymmetry of the fieldstrength tensor and the freedom to throw away total derivatives.
Abstract Format
html
Language
English
Format
Accession Number
TG03498
Shelf Location
Archives, The Learning Commons, 12F Henry Sy Sr. Hall
Physical Description
176 leaves ; 28 cm.
Keywords
Quantum field theory; Lagrangian functions; Calculus of variations; Differential equations; Dimensional theory (Topology)
Recommended Citation
Pagaran, J. G. (2003). Calculation of higher mass-dimensional effective Lagrangians in quantum field theory. Retrieved from https://animorepository.dlsu.edu.ph/etd_masteral/3079
