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Theta vacuum information


In quantum field theory, the theta vacuum is the semi-classical vacuum state of non-abelian Yang–Mills theories specified by the vacuum angle θ that arises when the state is written as a superposition of an infinite set of topologically distinct vacuum states. The dynamical effects of the vacuum are captured in the Lagrangian formalism through the presence of a θ-term which in quantum chromodynamics leads to the fine tuning problem known as the strong CP problem. It was discovered in 1976 by Curtis Callan, Roger Dashen, and David Gross,[1] and independently by Roman Jackiw and Claudio Rebbi.[2]

  1. ^ Callan, C.G.; Dashen, R.F.; Gross, D.J. (1976). "The structure of the gauge theory vacuum". Physics Letters B. 63 (3): 334–340. Bibcode:1976PhLB...63..334C. doi:10.1016/0370-2693(76)90277-X.
  2. ^ Jackiw, R.; Rebbi, C. (1976). "Vacuum Periodicity in a Yang–Mills Quantum Theory". Physical Review Letters. 37 (3): 172–175. Bibcode:1976PhRvL..37..172J. doi:10.1103/PhysRevLett.37.172.

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Theta vacuum

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quantum field theory, the theta vacuum is the semi-classical vacuum state of non-abelian Yang–Mills theories specified by the vacuum angle θ that arises when...

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Vacuum

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Suction – creation of a partial vacuum Theta vacuumvacuum state of semi-classical pure-Yang Mills theories Vactrain Vacuum cementing – natural process...

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Sphaleron

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in physics Instanton – Solitons in Euclidean spacetime Theta vacuum – Yang–Mills theory vacuum state Periodic instantons – Finite energy solutions in...

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Kerr metric

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{\frac {d\theta }{d\lambda }}&=\pm {\sqrt {\Theta (\theta )}}\\\Sigma {\frac {d\phi }{d\lambda }}&=-\left(aE-{\frac {L_{z}}{\sin ^{2}\theta }}\right)+{\frac...

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Vacuum Rabi oscillation

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A vacuum Rabi oscillation is a damped oscillation of an initially excited atom coupled to an electromagnetic resonator or cavity in which the atom alternately...

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Goldstone boson

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the vacuum, is at least m0, ‖ d d t | θ ⟩ ‖ = ‖ H | θ ⟩ ‖ ≥ m 0 ‖ | θ ⟩ ‖ . {\displaystyle \left\|{\frac {d}{dt}}|\theta \rangle \right\|=\|H|\theta \rangle...

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Wavelength

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have longer wavelengths. Wavelength depends on the medium (for example, vacuum, air, or water) that a wave travels through. Examples of waves are sound...

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Cherenkov radiation

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effects had never been experimentally observed. While the speed of light in vacuum is a universal constant (c = 299,792,458 m/s), the speed in a material may...

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Fresnel equations

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}=\left|{\frac {Z_{2}\cos \theta _{\mathrm {i} }-Z_{1}\cos \theta _{\mathrm {t} }}{Z_{2}\cos \theta _{\mathrm {i} }+Z_{1}\cos \theta _{\mathrm {t} }}}\right|^{2}...

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Refraction

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the angle of incidence θ 1 {\displaystyle {\theta _{1}}} and angle of refraction θ 2 {\displaystyle {\theta _{2}}} is equal to the ratio of phase velocities...

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Squeezed coherent state

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\zeta |{\hat {a}}|\alpha ,\zeta \rangle =\alpha cosh(r)-\alpha ^{*}e^{i\theta }sinh(r)} ⟨ α , ζ | a ^ 2 | α , ζ ⟩ = α 2 c o s h 2 ( r ) + α ∗ 2 e 2 i...

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Roman Jackiw

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Swarthmore Known for Adler–Bell–Jackiw anomaly Jackiw–Teitelboim gravity Theta vacuum Children Stefan Jackiw Nicholas Jackiw Awards Dirac Medal (1998) Heineman...

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Higgs mechanism

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z-axis takes the vacuum to   (   0   ,   v   e − 1 2   i   θ   )   . {\displaystyle \ {\Bigl (}\ 0\ ,\ v\ e^{-{\tfrac {1}{2}}\ i\ \theta }\ {\Bigr )}~.}...

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Wormhole

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{\displaystyle ds^{2}=-c^{2}\,dt^{2}+d\ell ^{2}+(k^{2}+\ell ^{2})(d\theta ^{2}+\sin ^{2}\theta \,d\varphi ^{2}),} first presented by Ellis (see Ellis wormhole)...

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Derivation of the Schwarzschild solution

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\theta ,\phi ,t)\rightarrow (r,\theta ,-\phi ,t)} and ( r , θ , ϕ , t ) → ( r , − θ , ϕ , t ) {\displaystyle (r,\theta ,\phi ,t)\rightarrow (r,-\theta...

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Schwarzschild metric

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θ = r s r , {\displaystyle 2R^{t}{}_{\theta \theta t}=2R^{r}{}_{\theta \theta r}=R^{\phi }{}_{\theta \phi \theta }={\frac {r_{\text{s}}}{r}},} 2 R t ϕ...

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Squeeze operator

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r-e^{-i\theta }{\hat {a}}\sinh r} The squeeze operator is ubiquitous in quantum optics and can operate on any state. For example, when acting upon the vacuum...

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Frequency

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{\displaystyle y(t)=\sin \theta (t)=\sin(\omega t)=\sin(2\mathrm {\pi } ft)} d θ d t = ω = 2 π f . {\displaystyle {\frac {\mathrm {d} \theta }{\mathrm {d} t}}=\omega...

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Trajectory

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{d} H \over \mathrm {d} \theta }=v^{2}2\cos(\theta )\sin(\theta )/(2g)} which is zero when θ = π / 2 = 90 ∘ {\displaystyle \theta =\pi /2=90^{\circ }} ....

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Curtis Callan

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CGHS model Callan–Treiman relation Contributions to instanton physics Theta vacuum Scientific career Institutions Princeton University Doctoral advisor...

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Electroweak interaction

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\\Z^{0}\end{pmatrix}}={\begin{pmatrix}\cos \theta _{\text{W}}&\sin \theta _{\text{W}}\\-\sin \theta _{\text{W}}&\cos \theta _{\text{W}}\end{pmatrix}}{\begin{p...

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Refractive index

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medium is λ = λ0/n, where λ0 is the wavelength of that light in vacuum. This implies that vacuum has a refractive index of 1, and assumes that the frequency...

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Gaussian function

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+2b\cdot \cos \theta \sin \theta +c\cdot \sin ^{2}\theta )}},\\\sigma _{Y}^{2}&={\frac {1}{2(a\cdot \sin ^{2}\theta -2b\cdot \cos \theta \sin \theta +c\cdot...

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Total internal reflection

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_{0}}{2\pi \,{\sqrt {n_{1}^{2}\sin ^{2}\theta _{\text{i}}\,-\,n_{2}^{2}}}}}~,} where λ0 is the wavelength in vacuum, i.e.  2 π / k 0 . {\displaystyle \,2\pi...

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Projectile motion

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\theta +\cos ^{2}\theta \cdot \ln {\frac {1+\sin \theta }{1-\sin \theta }}\right)={\frac {v_{0}^{2}}{g}}\left(\sin \theta +\cos ^{2}\theta \cdot...

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Composite material

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{\displaystyle T(\theta )_{\epsilon }={\begin{bmatrix}\cos ^{2}\theta &\sin ^{2}\theta &\cos \theta \sin \theta \\sin^{2}\theta &\cos ^{2}\theta &-\cos \theta \sin...

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Free spectral range

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\lambda ={\frac {\lambda _{0}^{2}}{2nl\cos \theta +\lambda _{0}}}\approx {\frac {\lambda _{0}^{2}}{2nl\cos \theta }},} where λ0 is the central wavelength...

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