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Finite Lattice Size Corrections The Energy-Momentum Dispersion

Title: Finite Lattice Size Corrections The Energy-Momentum Dispersion.
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Name(s): McDargh, Zachary, author
Physics
Type of Resource: text
Genre: Text
Issuance: serial
Date Issued: 2012
Physical Form: computer
online resource
Extent: 1 online resource
Language(s): English
Abstract/Description: Lattice Gauge Theory (LGT) describes gauge and matter fields on a discrete Euclidian space-time lattice. Due to the finite spacing between the lattice points, there is a built-in ultra-violet energy cutoff. Additionally, there is an infrared energy cutoff in computer simulations due to the finite size of the lattice. With these approximations, the energy-momentum dispersion becomes modified. In this thesis, we study the recovery of the continuous energy-momentum dispersion. We perform fits of the correlation function fromMarkov ChainMonte Carlo (MCMC) simulations for various lattice sizes and spacings for a free-scalar field and for an Abelian U(1) gauge field. For the scalar field, we also vary the mass of the particles; for U(1) LGT, we vary the coupling constant β. These fits return the energy of a particle at definite momentum, from which the mass can be recovered using the energy-momentum dispersion. It is found that the finite-size effect in MCMC calculations decreases as exp(−N), where N is the space dimension of the lattice. Furthermore, the effect is more significant for larger masses (scalar field) and coupling constant values near the phase transition βc = 1.01 (U(1) LGT).
Identifier: FSU_migr_uhm-0047 (IID)
Keywords: Lattice Gauge Theory (LGT)
Submitted Note: A Thesis submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Honors in the Major.
Degree Awarded: Spring Semester, 2012.
Date of Defense: December 1, 2011.
Subject(s): Physics
Persistent Link to This Record: http://purl.flvc.org/fsu/fd/FSU_migr_uhm-0047
Restrictions on Access: http://creativecommons.org/licenses/by-nc-nd/3.0/
Owner Institution: FSU
Is Part of Series: Honors Theses.

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McDargh, Z. (2012). Finite Lattice Size Corrections The Energy-Momentum Dispersion. Retrieved from http://purl.flvc.org/fsu/fd/FSU_migr_uhm-0047