scholarly journals Construction of the functional integral representation for fermion Green's functions

1977 ◽  
Author(s):  
D.E. Soper
Keyword(s):  
Integral Representation ◽  
Green's Functions ◽  
Green’S Functions ◽  
Functional Integral ◽  
Functional Integral Representation

THE FUNCTIONAL INTEGRAL ON THE HALF-LINE

1990 ◽  
Vol 05 (15) ◽  
pp. 3029-3051 ◽  
Author(s):  
EDWARD FARHI ◽  
SAM GUTMANN
Keyword(s):  
Time Evolution ◽  
Wide Class ◽  
Green's Functions ◽  
Green’S Functions ◽  
Functional Integral ◽  
Half Line ◽  
Functional Integrals ◽  
Quantum Hamiltonian ◽  
Do So

A quantum Hamiltonian, defined on the half-line, will typically not lead to unitary time evolution unless the domain of the Hamiltonian is carefully specified. Different choices of the domain result in different Green’s functions. For a wide class of non-relativistic Hamiltonians we show how to define the functional integral on the half-line in a way which matches the various Green’s functions. To do so we analytically continue, in time, functional integrals constructed with real measures that give weight to paths on the half-line according to how much time they spend near the origin.

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