Vacuum state - Citizendia

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In quantum field theory, the vacuum state (also called the vacuum) is the quantum state with the lowest possible energy. In quantum field theory (QFT the forces between particles are mediated by other particles Motivation and history When calculating Scattering cross sections in Particle physics, the interaction between particles can be described The history of quantum field theory starts with its creation by Dirac when he attempted to quantize the Electromagnetic field in the late 1920s In quantum field theory (QFT the forces between particles are mediated by other particles In Quantum physics, a quantum state is a mathematical object that fully describes a quantum system. In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός Generally, it contains no physical particles. The term "zero-point field" is sometimes used as a synonym for the vacuum state of an individual quantized field. In Quantum field theory, the zero-point field is the lowest energy state of a field, i

According to present-day understanding of what is called the vacuum state or the quantum vacuum, it is "by no means a simple empty space"^[1], and again: "it is a mistake to think of any physical vacuum as some absolutely empty void. "^[2] According to quantum mechanics, the vacuum state is not truly empty but instead contains fleeting electromagnetic waves and particles that pop into and out of existence. ^[3]^[4]^[5]

1 Non-vanishing vacuum state
2 The energy of the vacuum state
3 The symmetry of the vacuum state
4 Electrical permittivity of vacuum state
5 Notations
6 Virtual particles
7 References and notes
8 Further reading
9 See also

Non-vanishing vacuum state

If the quantum field theory can be accurately described through perturbation theory, then the properties of the vacuum are analogous to the properties of the ground state of a quantum mechanical harmonic oscillator (or more accurately, the ground state of a QM problem). This article describes perturbation theory as a general mathematical method In Quantum mechanics, a stationary state is an Eigenstate of a Hamiltonian, or in other words a state of definite energy This article is about the harmonic oscillator in classical mechanics In Quantum mechanics, a stationary state is an Eigenstate of a Hamiltonian, or in other words a state of definite energy In this case the vacuum expectation value (VEV) of any field operator vanishes. In Quantum field theory the vacuum expectation value (also called condensate) of an operator is its average Expected value in the vacuum In quantum field theory (QFT the forces between particles are mediated by other particles For quantum field theories in which perturbation theory breaks down at low energies (for example, Quantum chromodynamics or the BCS theory of superconductivity) field operators may have non-vanishing vacuum expectation values called condensates. This article describes perturbation theory as a general mathematical method Quantum chromodynamics (abbreviated as QCD is a theory of the Strong interaction ( color force a Fundamental force describing the interactions of the Superconductivity is a phenomenon occurring in certain Materials generally at very low Temperatures characterized by exactly zero electrical resistance In Quantum field theory the vacuum expectation value (also called condensate) of an operator is its average Expected value in the vacuum In Quantum field theory the vacuum expectation value (also called condensate) of an operator is its average Expected value in the vacuum In the Standard Model, the non-zero vacuum expectation value of the Higgs field, arising from spontaneous symmetry breaking, is the mechanism by which the other fields in the theory acquire mass. The Standard Model of Particle physics is a theory that describes three of the four known Fundamental interactions together with the Elementary particles The Higgs Boson is a hypothetical massive scalar Elementary particle predicted to exist by the Standard Model of Particle physics In Physics, spontaneous symmetry breaking occurs when a system that is symmetric with respect to some Symmetry group goes into a Vacuum state

The energy of the vacuum state

Main article: Vacuum energy

In many situations, the vacuum state can be defined to have zero energy, although the actual situation is considerably more subtle. Vacuum energy is an underlying background Energy that exists in Space even when devoid of Matter (known as Free space) The vacuum state is associated with a zero-point energy, and this zero-point energy has measurable effects. In Physics, the zero-point energy is the lowest possible Energy that a Quantum mechanical Physical system may possess and is the energy of the In the laboratory, it may be detected as the Casimir effect. In Physics, the Casimir effect and the Casimir-Polder force are physical forces arising from a quantized field. In physical cosmology, the energy of the vacuum state appears as the cosmological constant. Physical cosmology, as a branch of Astronomy, is the study of the large-scale structure of the Universe and is concerned with fundamental questions about its In Physical cosmology, the cosmological constant (usually denoted by the Greek capital letter Lambda: Λ was proposed by Albert Einstein as a modification An outstanding requirement imposed on a potential Theory of Everything is that the energy of the vacuum state must explain the physically observed cosmological constant. A theory of everything ( TOE) is a putative Theory of Theoretical physics that fully explains and links together all known physical phenomena

The symmetry of the vacuum state

For a relativistic field theory, the vacuum is Poincaré invariant. This page is about the scientific concept of relativity for philosophical or sociological theories about relativity see Relativism. In Physics and Mathematics, the Poincaré group, named after Henri Poincaré, is the group of isometries of Minkowski spacetime Poincaré invariance implies that only scalar combinations of field operators have non-vanishing VEVs. The VEV may break some of the internal symmetries of the Lagrangian of the field theory. In Physics, a field is a Physical quantity associated to each point of Spacetime. The Lagrangian, L of a Dynamical system is a function that summarizes the dynamics of the system In this case the vacuum has less symmetry than the theory allows, and one says that spontaneous symmetry breaking has occurred. In Physics, spontaneous symmetry breaking occurs when a system that is symmetric with respect to some Symmetry group goes into a Vacuum state See Higgs mechanism, standard model and Woit. The Higgs mechanism is Spontaneous symmetry breaking in a Gauge theory. The Standard Model of Particle physics is a theory that describes three of the four known Fundamental interactions together with the Elementary particles ^[6]

Electrical permittivity of vacuum state

In principle, it is possible for the experimental electrical permittivity ε of the vacuum state to deviate from the defined scalar value ε₀ of the electric constant due to quantum corrections to Maxwell's equations. Vacuum permittivity, referred to by international standards organizations as the electric constant, and denoted by the symbol ε0 is a fundamental Physical These theoretical developments are described, for example, in Dittrich and Gies. ^[5] In particular, the theory of quantum electrodynamics predicts that vacuum should exhibit nonlinear effects that will make it behave like a birefringent material with ε slightly greater than ε₀ for extremely strong electric fields. Quantum electrodynamics ( QED) is a relativistic Quantum field theory of Electrodynamics. Nonlinear optics (NLO is the branch of Optics that describes the behaviour of Light in nonlinear media, that is media in which the dielectric polarization Birefringence, or double refraction, is the decomposition of a ray of Light into two rays (the ordinary ray and the extraordinary ray ^[7]^[8] Explanations for dichroism from particle physics, outside quantum electrodynamics, also have been proposed. Dichroic redirects here For the filter see Dichroic filter. For the glass see Dichroic glass. ^[9] Active attempts to measure such effects have been unsuccessful so far. ^[10]

Notations

The vacuum state is written as $|0\rangle$ or $|\rangle$ . The VEV of a field φ, which should be written as $\langle0|\phi|0\rangle$ , is usually condensed to $\langle\phi\rangle$ .

Virtual particles

The uncertainty principle in the form $\Delta E\Delta t\ge\hbar$ implies that in the vacuum one or more particles with energy ΔE above the vacuum may be created for a short time Δt. In Quantum physics, the Heisenberg uncertainty principle states that locating a particle in a small region of space makes the Momentum of the particle uncertain These virtual particles are included in the definition of the vacuum. In Physics, a virtual particle is a particle that exists for a limited time and space introducing uncertainty in their energy and momentum due to the Heisenberg Uncertainty

References and notes

^ Astrid Lambrecht (Hartmut Figger, Dieter Meschede, Claus Zimmermann Eds. ) (2002). Observing mechanical dissipation in the quantum vacuum: an experimental challenge; in Laser physics at the limits. Berlin/New York: Springer, p. 197. ISBN 3540424180.
^ Christopher Ray (1991). Time, space and philosophy. London/New York: Routledge, Chapter 10, p. 205. ISBN 0415032210.
^ AIP Physics News Update,1996
^ Physical Review Focus Dec. 1998
^ ^a ^b Walter Dittrich & Gies H (2000). Probing the quantum vacuum: perturbative effective action approach. Berlin: Springer. ISBN 3540674284.
^ Peter Woit (2006). Not even wrong: the failure of string theory and the search for unity in physical law. New York: Basic Books. ISBN 0465092756.
^ Klein, James J. and B. P. Nigam, Birefringence of the vacuum, Physical Review vol. 135, p. B1279-B1280 (1964).
^ Mourou, G. A. , T. Tajima, and S. V. Bulanov, Optics in the relativistic regime; § XI Nonlinear QED, Reviews of Modern Physics vol. 78 (no. 2), 309-371 (2006).
^ Gies, H et al.: Polarized light propagating in a magnetic field as a probe for millicharged fermions Phys. Rev. Letts. 97 (2006) 140402
^ CC Davis et al. Experimental challenges involved in searches for ... nonlinear QED effects by sensitive optical techniques

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