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