Feyman's path integral without the "Path Integral": an antiminimal approach to quantum formalism

Date

5-2005

Degree

Bachelor of Science in Applied Physics

College

College of Arts and Sciences (CAS)

Adviser/Committee Chair

Allan L. Alinea

Abstract

We suggested an alternative interpretation and derivation of Feynman's Path Integral without the necessity of postulating an infinite contribution of all possible classical paths of a certain quantum. particle. We have done this by treating the probability amplitude G = cap (iS/h) not as a contribution of a particular path but as a set function that measures the area of a subspace S in a quantum phase space. The parameter S is considered not as the classical action of a particular path, but as a set of N possible number of quantum states the quantum particle can take in transition between two points in space. The probability amplitude G is not postulated ad hoc to obey certain mathematical rules but uses properties of a set function. In this way, we eliminated the complexity of deriving Feynman's "Sum Over Histories"' using the sum formula of a geometric series and a certain Gaussian integral. The main difference however is a single path is realized defined by infinite number of points in a given region in space. Feynman's minimal approach of treating G as mere mathematical tool for representation of paths and devoid of any physical meaning is never realized. It is viewed here (in its Hamiltonian form i.e. h = 1) not only as a set function but interpreted as an explicit mathematical representation of quantum state obeying Heisenberg's Indeterminacy Relation. The operator correspondence of observable is interpreted as mere indication of the indeterminate status of the observable and consequence of a complex representation of observable. Lastly a new quantum interpretation is realized.

Language

English

Location

UPLB Main Library Special Collections Section (USCS)

Call Number

Thesis

Document Type

Thesis

This document is currently not available here.

Share

COinS