Computational Physics

Table 12.2.

Meaning of several physical quantities in different interpretations of the path integral.

Quantum mechanics

Quantum statistical mechanics

Classical mechanics

Statistical physics

d-dimensional

d-dimensional

d-dimensional subspace

d-dimensional

configuration space

configuration space

of configuration space

configuration space

imaginary time

τ

inverse temperature

1-dimensional axis

inverse temperature

β

=

1 /

kB

T

in configuration space

β

=

1 /

kB

T

time-evolution operator

Boltzmann operator e

−β

H

• 
  

transfer matrix

kinetic energy

kinetic energy

harmonic interparticle potential

inter-row coupling of

transfer matrix

Lagrangian

Lagrangian

Lagrangian

Hamiltonian

path integral

quantum partition function

• 
  

partition function

of

d-dimensional system

of (

d

+

1)-dimensional system

classical limit

zero temperature

stationary path

zero temperature