Institute of Theoretical Physics · Faculty of Mathematics and Physics, Charles University
Master's thesis, University of Alberta (1997)
The main goal of this work is an investigation of relationships between
the quantum theory of a scalar field and the quantum mechanics of
a relativistic particle in a general spacetime.
Quantum field theory of a scalar field on a time-bounded domain is
formulated using canonical quantization. Special attention is paid to
boundary conditions and their implication for the interpretation of
the theory. The relationship between configuration, particle and
holomorphic representations is found. It is shown that all
important structures can be reconstructed from knowledge of
Green functions satisfying certain conditions. Transition
amplitudes are expressed using such Green functions, and their
structure is discussed.
The field theory is also reformulated using boundary quantum
mechanics in which initial and final conditions play equivalent roles.
This formulation is more suitable for the path integral approach
and for the Euclidian version of the theory in which there is no preferred
time flow. Also a derivation of transition amplitudes is much more
straightforward in this formalism.
Next the quantum mechanics of a relativistic particle is
formulated using the sum-over-histories approach. The theory is again
investigated in a time-bounded domain, and boundary conditions are
discussed. It is shown that the quantum mechanics of a relativistic
particle leads to a many-particle theory and that transition amplitudes
have the same structure as in the QFT of a scalar field. This connection
allows one to identify these two theories. The relationship
between boundary conditions needed for QM of a relativistic particle
and the particle interpretation of QFT of a scalar field is investigated.
Ph.D. thesis
@mastersthesis{UTF11,
author = {Krtouš, P.},
title = {{Relationships between Scalar Field and Relativistic Particle Quantizations}},
school = {University of Alberta},
volume = {0},
year = {1997},
month = {9},
note = {Ph.D. thesis},
}