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The result is that the set of vacua of the quantum theory is generally much smaller than that of the classical theory. A notable exception occurs when the various vacua in question are related by a symmetry which guarantees that their energy levels remain exactly degenerate. The situation is very different in supersymmetric quantum field ...
the mass–energy equivalence formula which gives the energy in terms of the momentum and the rest mass of a particle. The equation for the mass shell is also often written in terms of the four-momentum ; in Einstein notation with metric signature (+,−,−,−) and units where the speed of light c = 1 {\displaystyle c=1} , as p μ p μ ≡ p ...
A proven no-go theorem indicates this situation, called the Quintom scenario, requires at least two degrees of freedom for dark energy models involving ideal gases or scalar fields. [ 21 ] In 2024, more detailed data from the Dark Energy Spectroscopic Instrument provided evidence suggesting a possible "Quintom-B" scenario, with the equation of ...
A scalar field is invariant under any Lorentz transformation. [1] The only fundamental scalar quantum field that has been observed in nature is the Higgs field. However, scalar quantum fields feature in the effective field theory descriptions of many physical phenomena.
The New Quantum Age: From Bell's Theorem to Quantum Computation and Teleportation, Oxford University Press, 2011, ISBN 978-0-19-958913-5; Stephen Hawking. The Dreams that Stuff is Made of, Running Press, 2011, ISBN 978-0-76-243434-3; A. Douglas Stone. Einstein and the Quantum, the Quest of the Valiant Swabian, Princeton University Press, 2006.
This is a list of quantum field theories. The first few sections are organized according to their matter content, that is, the types of fields appearing in the theory. This is just one of many ways to organize quantum field theories, but reflects the way the subject is taught pedagogically.
The energy content of this volume element at 5 km from the station is 2.1 × 10 −10 × 0.109 = 2.3 × 10 −11 J, which amounts to 3.4 × 10 14 photons per (). Since 3.4 × 10 14 > 1, quantum effects do not play a role. The waves emitted by this station are well-described by the classical limit and quantum mechanics is not needed.
Ishiwara was one of the first Japanese scholars to turn to the theory of relativity; he wrote the first scientific article in Japan on this subject. [3] In 1909-1911, he studied within the framework of this theory a number of specific problems related to the dynamics of electrons, the propagation of light in moving objects and the calculation of the energy-momentum tensor of the ...