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Full-Text Articles in Quantum Physics
Zeta Function Regularization And Its Relationship To Number Theory, Stephen Wang
Zeta Function Regularization And Its Relationship To Number Theory, Stephen Wang
Electronic Theses and Dissertations
While the "path integral" formulation of quantum mechanics is both highly intuitive and far reaching, the path integrals themselves often fail to converge in the usual sense. Richard Feynman developed regularization as a solution, such that regularized path integrals could be calculated and analyzed within a strictly physics context. Over the past 50 years, mathematicians and physicists have retroactively introduced schemes for achieving mathematical rigor in the study and application of regularized path integrals. One such scheme was introduced in 2007 by the mathematicians Klaus Kirsten and Paul Loya. In this thesis, we reproduce the Kirsten and Loya approach to …
Dynamics For Discretized Gravity In The Causal Set Approach, Benjamin Pilgrim
Dynamics For Discretized Gravity In The Causal Set Approach, Benjamin Pilgrim
Electronic Theses and Dissertations
Causal set theory is an approach to quantum gravity which replaces the continuous spacetime manifold with a discrete set of points and a partial order. In this work, I will focus on causal sets embeddable in two-dimensional manifolds, and define an action based on chains which in the continuum limit replicates the Einstein-Hilbert action; furthermore, I will propose a variational principle based on this action and numerically show it can distinguish nonflat manifoldlike causal sets from the most common type of nonmanifoldlike causal sets. I will then supplement this action with a boundary term similar to the Gibbons-Hawking-York boundary term …