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confused_nevin
edit approved Jul 16 at 12:12
confused_nevin
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In Altland and Simons' "Condensed Matter Field Theory" book, on the partition function for the non-interacting gas section, is states:

enter image description here

howeverstated that, after diagonalizing the hamiltonian the action assumes the form $$ S = \sum_a \sum_{\omega_n} \overline \phi_{an} (-i \omega_n + \xi_a) \phi_{an} $$ where $\xi_a \equiv \epsilon_a - \mu$ and $\epsilon_a$ are the single-particle energies. However, immediately after that, a beta factor shows up when computing the Path Integral:

enter image description here

where $$ \mathcal Z_a = \int D(\overline\phi_a, \phi_a) e^{-\sum_n \overline \phi_{an} (-i \omega_n + \xi_a) \phi_{an}} = \prod_n [\beta(-i \omega_n + \xi_a)]^{-\zeta} $$ where $\zeta =1 (−1)$ for bosonic (fermionic) fields, respectively.

Where is that $\beta$ factor coming from?

In Altland and Simons' "Condensed Matter Field Theory" book, on the partition function for the non-interacting gas section, is states:

enter image description here

however, immediately after that, a beta factor shows up when computing the Path Integral:

enter image description here

where $\zeta =1 (−1)$ for bosonic (fermionic) fields, respectively.

Where is that $\beta$ factor coming from?

In Altland and Simons' "Condensed Matter Field Theory" book, on the partition function for the non-interacting gas section, is stated that, after diagonalizing the hamiltonian the action assumes the form $$ S = \sum_a \sum_{\omega_n} \overline \phi_{an} (-i \omega_n + \xi_a) \phi_{an} $$ where $\xi_a \equiv \epsilon_a - \mu$ and $\epsilon_a$ are the single-particle energies. However, immediately after that, a beta factor shows up when computing the Path Integral: $$ \mathcal Z_a = \int D(\overline\phi_a, \phi_a) e^{-\sum_n \overline \phi_{an} (-i \omega_n + \xi_a) \phi_{an}} = \prod_n [\beta(-i \omega_n + \xi_a)]^{-\zeta} $$ where $\zeta =1 (−1)$ for bosonic (fermionic) fields, respectively.

Where is that $\beta$ factor coming from?

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Qmechanic ♦
Qmechanic ♦
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How does the $\beta$ factor appear in eq. (4.33) of AtlandAltland, Simons "Condensed Matter Field Theory"?

In AtlandAltland and Simons' "Condensed Matter Field Theory" book, on the partition function for the non-interacting gas section, is states:

enter image description here

however, immediately after that, a beta factor shows up when computing the Path Integral:

enter image description here

where $\zeta =1 (−1)$ for bosonic (fermionic) fields, respectively.

Where is that $\beta$ factor coming from?

How does the $\beta$ factor appear in eq. (4.33) of Atland, Simons "Condensed Matter Field Theory"?

In Atland and Simons' "Condensed Matter Field Theory" book, on the partition function for the non-interacting gas section, is states:

enter image description here

however, immediately after that, a beta factor shows up when computing the Path Integral:

enter image description here

where $\zeta =1 (−1)$ for bosonic (fermionic) fields, respectively.

Where is that $\beta$ factor coming from?

How does the $\beta$ factor appear in eq. (4.33) of Altland, Simons "Condensed Matter Field Theory"?

In Altland and Simons' "Condensed Matter Field Theory" book, on the partition function for the non-interacting gas section, is states:

enter image description here

however, immediately after that, a beta factor shows up when computing the Path Integral:

enter image description here

where $\zeta =1 (−1)$ for bosonic (fermionic) fields, respectively.

Where is that $\beta$ factor coming from?

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Qmechanic ♦
Qmechanic ♦
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How does the beta$\beta$ factor appear in eq. 4(4.33) of Atland, Simons "Condensed Matter Field Theory"?

In Atland and Simons' "Condensed Matter Field Theory" book, on the partition function for the non-interacting gas section, is states:

enter image description here

however, immediately after that, a beta factor shows up when computing the Path Integral:

enter image description here

where $\zeta =1 (−1)$ for bosonic (fermionic) fields, respectively.

Where is that beta$\beta$ factor coming from  ?

How does the beta factor appear in eq. 4.33 of Atland, Simons "Condensed Matter Field Theory"?

In Atland and Simons' "Condensed Matter Field Theory" book, on the partition function for the non-interacting gas section, is states:

enter image description here

however, immediately after that, a beta factor shows up when computing the Path Integral:

enter image description here

Where is that beta coming from  ?

How does the $\beta$ factor appear in eq. (4.33) of Atland, Simons "Condensed Matter Field Theory"?

In Atland and Simons' "Condensed Matter Field Theory" book, on the partition function for the non-interacting gas section, is states:

enter image description here

however, immediately after that, a beta factor shows up when computing the Path Integral:

enter image description here

where $\zeta =1 (−1)$ for bosonic (fermionic) fields, respectively.

Where is that $\beta$ factor coming from?

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