## Zero Point Energy

by | on March 7, 2012

### The uncertainty principle requires every physical system to have a zero point energy greater than the minimum of its classical potential well, even at absolute zero.

Vacuum energy is the zero point energy of all the fields in space, which in the Standard Model includes the electromagnetic field, other gauge fields, fermionic fields, and the Higgs field.

It is the energy of the vacuum, which in quantum field theory is defined not as empty space but as the ground state of the fields. In cosmology, the vacuum energy is one possible explanation for the cosmological constant.

A related term is zero point field, which is the lowest energy state of a particular field.In ordinary quantum mechanics, the zero point energy is the energy associated with the ground state of the system. The professional physics literature tends to measure frequency, as denoted by ν above, using angular frequency, denoted with ω and defined by ω = 2πν.

This leads to a convention of writing Planck’s constant h with a bar through its top to denote the quantity h/2π. In those terms, the most famous such example of zero-point energy is E={\hbar\omega / 2} associated with the ground state of the quantum harmonic oscillator.

In quantum mechanical terms, the zero-point energy is the expectation value of the Hamiltonian of the system in the ground state.In quantum field theory, the fabric of space is visualized as consisting of fields, with the field at every point in space and time being a quantum harmonic oscillator, with neighboring oscillators interacting.

In this case, one has a contribution of E={\hbar\omega / 2} from every point in space, resulting in a calculation of infinite zero-point energy in any finite volume; this is one reason renormalization is needed to make sense of quantum field theories. The zero-point energy is again the expectation value of the Hamiltonian; here, however, the phrase vacuum expectation value is more commonly used, and the energy is called the vacuum energy.

In quantum perturbation theory, it is sometimes said that the contribution of one-loop and multi-loop Feynman diagrams to elementary particle propagators are the contribution of vacuum fluctuations or the zero point energy to the particle masses.

<a title="Zero-point energy is the lowest possible energy that a quantum mechanical physical system may have; it is the energy of its ground state. All quantum mechanical systems undergo fluctuations even in their ground state and have an associated zero-point energy, a consequence of their wave-like nature. The uncertainty principle requires every physical system to have a zero-point energy greater than the minimum of its classical potential well, even at absolute zero.
Vacuum energy is the zero-point energy of all the fields in space, which in the Standard Model includes the electromagnetic field, other gauge fields, fermionic fields, and the Higgs field. It is the energy of the vacuum, which in quantum field theory is defined not as empty space but as the ground state of the fields. In cosmology, the vacuum energy is one possible explanation for the cosmological constant.[3] A related term is zero-point field, which is the lowest energy state of a particular field.

In ordinary quantum mechanics, the zero-point energy is the energy associated with the ground state of the system. The professional physics literature tends to measure frequency, as denoted by ν above, using angular frequency, denoted with ω and defined by ω = 2πν. This leads to a convention of writing Planck’s constant h with a bar through its top to denote the quantity h/2π. In those terms, the most famous such example of zero-point energy is E={\hbar\omega / 2} associated with the ground state of the quantum harmonic oscillator. In quantum mechanical terms, the zero-point energy is the expectation value of the Hamiltonian of the system in the ground state.

In quantum field theory, the fabric of space is visualized as consisting of fields, with the field at every point in space and time being a quantum harmonic oscillator, with neighboring oscillators interacting. In this case, one has a contribution of E={\hbar\omega / 2} from every point in space, resulting in a calculation of infinite zero-point energy in any finite volume; this is one reason renormalization is needed to make sense of quantum field theories. The zero-point energy is again the expectation value of the Hamiltonian; here, however, the phrase vacuum expectation value is more commonly used, and the energy is called the vacuum energy.

In quantum perturbation theory, it is sometimes said that the contribution of one-loop and multi-loop Feynman diagrams to elementary particle propagators are the contribution of vacuum fluctuations or the zero-point energy to the particle masses.” href=”http://www.facebook.com/ZP.Energy” rel=”theater”>

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