How to apply cutoff in path integral?
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I am working on harmonic oscillator for quantum fluctuations (apart from clasical part), path may written as
This may written as
for after Wick rotation. Boundary conditions must hold
,then I may use the Fourier transform to define eigenvectors.
And the eigenvector is
Then I may write
But eq(1) is obviously divergent for
How am I suppose to manage that? Should I apply any cutoff
This may written as
for after Wick rotation. Boundary conditions must hold
,then I may use the Fourier transform to define eigenvectors.
And the eigenvector is
Then I may write
But eq(1) is obviously divergent for
How am I suppose to manage that? Should I apply any cutoff
Answered by
0
I need to evaluate the Kernel K(qf,T;qi,0)=∫[dq]exp(Sq)K(qf,T;qi,0)=∫[dq]exp(Sq) I suppose this should give me finite solution. Classical part of this Kernel is finite and I'm wondering this should also be finite or regularize somehow.
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