Course of lectures on quantum fluctuations

Course content

  • Maxwell equations for macroscopic electrodynamics

  • Separation of electric and magnetic modes

  • Action and Lagrangian for macroscopic electrodynamics

  • Quantum vacuum energy

  • Green's function, Green's dyadic

  • Multiple scattering formalism, Stress tensor method

  • Lifshitz energy

  • Elbaum-Schick systems

Attendance list: Mathias Boström, Iver Brevik, Prachi Parashar, K. V. Shajesh, Subhojit Pal, John Joseph Marchetta, Niranjan Warnakulasooriya, Venkat Abhignan, and Aryan Illiat.

Lecture 1: Kramers-Kronig relation for response functions, Feb. 10, 2024

Presenter: Prof. K. V. Shajesh

Southern Illinois University--Carbondale, USA

Meeting notes

Lecture content

  • Contents of first ten equations in emthin.

  • Examples, like Drude model, plasma model, and Drude-Lorentz model, were not discussed in detail.

Discussion

  • In axion electrodynamics, the electric (magnetic) polarization gets a response from the magnetic (electric) field. The implications of the causal nature of this response should be investigated. Look up literature.

Lecture 2: Correlation function, Feb. 17, 2024

Presenter: Prof. K. V. Shajesh

Southern Illinois University--Carbondale, USA

Meeting notes

Lecture content

  • Schwinger's quantum action principle

  • Correlations are described by Green's function

  • Zero-dimension example: Harmonic oscillator forced by a noise (not satisfactorily completed)

Discussion

  • The divergences in the single-body Casimir energy of a dielectric ball are known to cancel out for mediums εμ=1. Could this feature be derived as a generic statement at the formalism level for an arbitrary single body?

  • Use our ideas in arXiv:1709.06284 and arXiv:2105.05507 to evaluate conclusions similar to those by Barrow in arXiv:2004.09444. For example, can we derive the horizon radius of a blackhole constructed out of self-similar concentric spheres?

Lecture 3: Maxwell equations, Feb. 24, 2024

Presenter: Prof. K. V. Shajesh

Southern Illinois University--Carbondale, USA

Meeting notes

Lecture content

  • Maxwell equations

  • Lagrangian for macroscopic electrodynamics

  • Dielectric function is Hermitian

Discussion

  • What is the physical interpretation of the external Polarization source?

  • Are fluctuations in polarization sources or the fluctuations in the fields the origins of zero point energy?

  • How is the dielectric function being Hermitian compatible with Kramers-Kronig relation? The hermitianity requires the principal dielectric components to be real. Thus, it does not allow dissipation. However, we will assume a small amount of dissipation to accommodate causality. This will then lead to a fluctuation-dissipation theorem.

Lecture 4: Quantum vacuum energy, March. 2, 2024

Presenter: Prof. K. V. Shajesh

Southern Illinois University--Carbondale, USA

Meeting notes

Lecture content

  • Variation in dynamical fields, source function, and background potential.

  • Green's dyadic

  • Quantum vacuum energy

Discussion

  • Derive the expression for quantum vacuum energy, presuming magnetic monopoles are allowed in the theory, and the magnetic source function is switched on.

  • Does the action formulation in terms of frequency allow one to attend problems that are out of equilibrium? Is Schwinger-Keldysh method about this.

  • The variation in the action due to variation in the background potential is functional. For a given body, can we use the idea of the calculus of variation to find the surface that minimizes the Casimir energy?