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Dirac`s coincidences sixty years on
Dirac`s coincidences sixty years on

... values span more than 100 orders of magnitude and come from an expression that is sensitively dependent on just one free parameter. Despite this, the suspicion remains that these successes are themselves mere “coincidences”. But we can find glimmerings of a solid fieldtheoretic basis if we rewrite ( ...
On Absolute Units, I: Choices - MIT Center for Theoretical Physics
On Absolute Units, I: Choices - MIT Center for Theoretical Physics

... he called a system of absolute units, based on the speed of light c, Newton’s gravitational constant G, and his newly minted quantum of action \. From these, by taking powers and ratios, one can manufacture units of mass MPlanck ! =\c/G ⊂ 2.2 × 10⊗5 gram, length LPlanck ! =\G/c3 ⊂ 1.6 × 10⊗33 centim ...
Generalized Momentum Operators
Generalized Momentum Operators

Second quantization and tight binding models
Second quantization and tight binding models

Queens College Department of Physics - Qc.edu
Queens College Department of Physics - Qc.edu

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Unruh Effect in Closed String Theory
Unruh Effect in Closed String Theory

... We have already obtained the solution of Klein-Gordon eq. in Minkowski Space-time. If we can represent the solution of Klein-Gordon eq. in Rindler space-time by the combination of the solutions of Klein-Gordon eq. in Minkowski space-time, it would be OK! Minkowski ...
Topological Coherence and Decoherence
Topological Coherence and Decoherence

... We are interested in topological field theories because they possess ‘hidden’ topological quantum numbers which are conserved even when the system is subject to quite severe perturbations. A model of central interest is the ‘dissipative W.A.H. model’ (named after Wannier, Az’bel, & Hofstadter’). Thi ...
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Hamiltonian Mechanics and Symplectic Geometry

... The first equation just says that the momentum is the mass times the velocity, combining this with the second equation is just the familiar F = −∇V = ma A special case of this occurs when V is quadratic q, this is the case of the harmonic oscillator, which can be solved exactly. The harmonic oscilla ...
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Physics and the Integers - damtp

... dirty, systems. The quantum Hall effect is a phenomenon that occurs when semiconductors are placed in a magnetic field at low temperatures. The Hall conductivity, which describes how current flows perpendicular to an applied electric field, is given by e2 σ=n h where e is the electron charge and h i ...
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Physical Laws of Nature vs Fundamental First Principles

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Scalar field theory

In theoretical physics, scalar field theory can refer to a classical or quantum theory of scalar fields. A scalar field is invariant under any Lorentz transformation.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. An example is the pion, which is actually a pseudoscalar.Since they do not involve polarization complications, scalar fields are often the easiest to appreciate second quantization through. For this reason, scalar field theories are often used for purposes of introduction of novel concepts and techniques.The signature of the metric employed below is (+, −, −, −).
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