‘‘Direct’’ calculation of quantum mechanical rate constants via path integral methods: Application to the reaction path Hamiltonian, with numerical test for the H+H2reaction in 3D

1985 ◽  
Vol 82 (12) ◽  
pp. 5475-5484 ◽  
Author(s):  
Koichi Yamashita ◽  
William H. Miller
Keyword(s):  
Path Integral ◽  
Rate Constants ◽  
Reaction Path ◽  
Numerical Test ◽  
Direct Calculation ◽  
Quantum Mechanical ◽  
Integral Methods ◽  
Reaction Path Hamiltonian

scholarly journals COORDINATE-INVARIANT PATH INTEGRAL METHODS IN CONFORMAL FIELD THEORY

2006 ◽  
Vol 21 (17) ◽  
pp. 3525-3563 ◽  
Author(s):  
ANDRÉ VAN TONDER
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Path Integral ◽  
Direct Calculation ◽  
Conformal Anomaly ◽  
Operator Formalism ◽  
Conformal Field ◽  
Integral Methods ◽  
Change Of Variables ◽  
Definition Of

We present a coordinate-invariant approach, based on a Pauli–Villars measure, to the definition of the path integral in two-dimensional conformal field theory. We discuss some advantages of this approach compared to the operator formalism and alternative path integral approaches. We show that our path integral measure is invariant under conformal transformations and field reparametrizations, in contrast to the measure used in the Fujikawa calculation, and we show the agreement, despite different origins, of the conformal anomaly in the two approaches. The natural energy–momentum in the Pauli–Villars approach is a true coordinate-invariant tensor quantity, and we discuss its nontrivial relationship to the corresponding nontensor object arising in the operator formalism, thus providing a novel explanation within a path integral context for the anomalous Ward identities of the latter. We provide a direct calculation of the nontrivial contact terms arising in expectation values of certain energy–momentum products, and we use these to perform a simple consistency check confirming the validity of the change of variables formula for the path integral. Finally, we review the relationship between the conformal anomaly and the energy–momentum two-point functions in our formalism.

Convenient and accurate discretized path integral methods for equilibrium quantum mechanical calculations

1981 ◽  
Vol 75 (3) ◽  
pp. 1347-1364 ◽  
Author(s):  
Kenneth S. Schweizer ◽  
Richard M. Stratt ◽  
David Chandler ◽  
Peter G. Wolynes
Keyword(s):  
Path Integral ◽  
Quantum Mechanical ◽  
Quantum Mechanical Calculations ◽  
Integral Methods

Quantum mechanical integral cross sections and rate constants for the F+HD reactions

2000 ◽  
Vol 112 (22) ◽  
pp. 9802-9809 ◽  
Author(s):  
Dong H. Zhang ◽  
Soo-Y. Lee ◽  
Michael Baer
Keyword(s):  
Cross Sections ◽  
Rate Constants ◽  
Quantum Mechanical

On evaluating the reaction path Hamiltonian

1988 ◽  
Vol 88 (2) ◽  
pp. 922-935 ◽  
Author(s):  
Michael Page ◽  
James W. McIver
Keyword(s):  
Reaction Path ◽  
Reaction Path Hamiltonian
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