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Imaginary time is a mathematical representation of time that appears in some approaches to special relativity and quantum mechanics. It finds uses in certain cosmological theories. Mathematically, imaginary time is real time which has undergone a Wick rotation so that its coordinates are multiplied by the imaginary unit i .
The magnetic flux frozen in a loop/hole (plus its λ L-layer) will always be quantized. However, the value of the flux quantum is equal to Φ 0 only when the path/trajectory around the hole described above can be chosen so that it lays in the superconducting region without screening currents, i.e. several λ L away from the surface
In quantum mechanics, the probability current (sometimes called probability flux) is a mathematical quantity describing the flow of probability. Specifically, if one thinks of probability as a heterogeneous fluid, then the probability current is the rate of flow of this fluid.
A fundamental physical constant occurring in quantum mechanics is the Planck constant, h. ... i is the imaginary unit; t = time; General time-dependent case: ...
[8] [9] In this Euclidean field theory, real-time observables can be retrieved by analytic continuation. [10] The Feynman rules for gauge theories in the Euclidean time formalism, were derived by C. W. Bernard. [8] The Matsubara formalism, also referred to as imaginary time formalism, can be extended to systems with thermal variations.
In thermal quantum field theory, bosonic and fermionic quantum fields () are respectively periodic or antiperiodic in imaginary time , with periodicity = /. Matsubara summation refers to the technique of expanding these fields in Fourier series
Wick rotation connects statistical mechanics to quantum mechanics by replacing inverse temperature with imaginary time, or more precisely replacing 1/k B T with it/ħ, where T is temperature, k B is the Boltzmann constant, t is time, and ħ is the reduced Planck constant. For example, consider a quantum system whose Hamiltonian H has ...
Σ is meant to indicate the physical space (usually, d = 3 for standard physics) and the extra dimension in Σ × I is "imaginary" time. The space Z(Σ) is the Hilbert space of the quantum theory and a physical theory, with a Hamiltonian H, will have a time evolution operator e itH or an "imaginary time" operator e −tH.