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E4. Free Fall

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Coherent State Path Integrals

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Gravity originates from variable energy density of

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... sense quantum gravity may be conceived of as any theory which couples general relativity (and thus a classical description of gravity) with quantum theory. I argue that the expectation –which serves as a motivation for quantum gravity in the broad sense – that general relativity and quantum theory m ...
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IOSR Journal of Mathematics (IOSR-JM)

... measuring apparatus itself as a quantum entity, which is a part of the entire quantum system consisting of the original system under observation together with this measuring apparatus. The apparatus is, after all, constructed in terms of the continuous and deterministic U. How, then, can the discont ...
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Tree Search and Quantum Computation

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CAUSALITY AND DISPERSION RELATIONS

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Polynomial-Time Algorithms for Prime Factorization and Discrete

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Quantum group

In mathematics and theoretical physics, the term quantum group denotes various kinds of noncommutative algebra with additional structure. In general, a quantum group is some kind of Hopf algebra. There is no single, all-encompassing definition, but instead a family of broadly similar objects.The term ""quantum group"" first appeared in the theory of quantum integrable systems, which was then formalized by Vladimir Drinfeld and Michio Jimbo as a particular class of Hopf algebra. The same term is also used for other Hopf algebras that deform or are close to classical Lie groups or Lie algebras, such as a `bicrossproduct' class of quantum groups introduced by Shahn Majid a little after the work of Drinfeld and Jimbo.In Drinfeld's approach, quantum groups arise as Hopf algebras depending on an auxiliary parameter q or h, which become universal enveloping algebras of a certain Lie algebra, frequently semisimple or affine, when q = 1 or h = 0. Closely related are certain dual objects, also Hopf algebras and also called quantum groups, deforming the algebra of functions on the corresponding semisimple algebraic group or a compact Lie group.Just as groups often appear as symmetries, quantum groups act on many other mathematical objects and it has become fashionable to introduce the adjective quantum in such cases; for example there are quantum planes and quantum Grassmannians.
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