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Basics of Lattice Quantum Field Theory∗
Basics of Lattice Quantum Field Theory∗

... prove rigorously that confinement persists in the continuum limit β → ∞ [this will win you a prestigeous prize!] ...
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... breaking? The answer is yes [5]. When dealing with the local supersymmetry transformation, we will inevitably encounter gravity interaction, since supersymmetry generator is related with spacetime transformation in the supersymmetry algebra. Like other gauge transformation, we need to introduce a ”m ...
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Vacuum and nonvacuum black holes in a uniform magnetic field

... in the linear case (15) but it should apply to neutral or charged generic configurations too where f expands as f 1r + f 2 + power series in 1/r , as are the cases with the Ayón-Beato–García static black hole [12], the solutions derived in [17,24], and the black holes of the f (T ) [23] and f (R) [2 ...
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CLASSICAL FIELDS - Instituto de Física Teórica

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WHAT IS THE CAUSE OF INERTIA?

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classical theoretical physics II

< 1 ... 3 4 5 6 7 8 9 10 11 ... 23 >

Kaluza–Klein theory

In physics, Kaluza–Klein theory (KK theory) is a unified field theory of gravitation and electromagnetism built around the idea of a fifth dimension beyond the usual four of space and time. It is considered to be an important precursor to string theory.The five-dimensional theory was developed in three steps. The original hypothesis came from Theodor Kaluza, who sent his results to Einstein in 1919, and published them in 1921. Kaluza's theory was a purely classical extension of general relativity to five dimensions. The 5-dimensional metric has 15 components. Ten components are identified with the 4-dimensional spacetime metric, 4 components with the electromagnetic vector potential, and one component with an unidentified scalar field sometimes called the ""radion"" or the ""dilaton"". Correspondingly, the 5-dimensional Einstein equations yield the 4-dimensional Einstein field equations, the Maxwell equations for the electromagnetic field, and an equation for the scalar field. Kaluza also introduced the hypothesis known as the ""cylinder condition"", that no component of the 5-dimensional metric depends on the fifth dimension. Without this assumption, the field equations of 5-dimensional relativity are enormously more complex. Standard 4-dimensional physics seems to manifest the cylinder condition. Kaluza also set the scalar field equal to a constant, in which case standard general relativity and electrodynamics are recovered identically.In 1926, Oskar Klein gave Kaluza's classical 5-dimensional theory a quantum interpretation, to accord with the then-recent discoveries of Heisenberg and Schrödinger. Klein introduced the hypothesis that the fifth dimension was curled up and microscopic, to explain the cylinder condition. Klein also calculated a scale for the fifth dimension based on the quantum of charge.It wasn't until the 1940s that the classical theory was completed, and the full field equations including the scalar field were obtained by three independent research groups:Thiry, working in France on his dissertation under Lichnerowicz; Jordan, Ludwig, and Müller in Germany, with critical input from Pauli and Fierz; and Scherrer working alone in Switzerland. Jordan's work led to the scalar-tensor theory of Brans & Dicke; Brans and Dicke were apparently unaware of Thiry or Scherrer. The full Kaluza equations under the cylinder condition are quite complex, and most English-language reviews as well as the English translations of Thiry contain some errors. The complete Kaluza equations were recently evaluated using tensor algebra software.
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