For other uses, see Normal order (disambiguation).
In quantum field theory a product of quantum fields, or equivalently their creation and annihilation operators, is usually said to be normal ordered (also called Wick order) when all creation operators are to the left of all annihilation operators in the product. The process of putting a product into normal order is called normal ordering (also called Wick ordering). The terms antinormal order and antinormal ordering are analogously defined, where the annihilation operators are placed to the left of the creation operators.
Normal ordering of a product of quantum fields or creation and annihilation operators can also be defined in many other ways. Which definition is most appropriate depends on the expectation values needed for a given calculation. Most of this article uses the most common definition of normal ordering as given above, which is appropriate when taking expectation values using the vacuum state of the creation and annihilation operators.
The process of normal ordering is particularly important for a quantum mechanical Hamiltonian. When quantizing a classical Hamiltonian there is some freedom when choosing the operator order, and these choices lead to differences in the ground state energy. That's why the process can also be used to eliminate the infinite vacuum energy of a quantum field.
evaluation order would have terminated without error. The name "normalorder" comes from the lambda calculus, where normalorder reduction will find a normal form...
Normal(s) or The Normal(s) may refer to: Look up normal in Wiktionary, the free dictionary. Normal (2003 film), starring Jessica Lange and Tom Wilkinson...
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued...
non-renewed game cards. Lego Universe became available for normalorder on October 27, 2010. The NormalOrder shipped with only the Lego Universe DVD and one month...
In number theory, a normalorder of an arithmetic function is some simpler or better-understood function which "usually" takes the same or closely approximate...
reduced. If a term has a beta-normal form, normalorder reduction will always reach that normal form. Applicative order The leftmost innermost redex is...
winners are determined for the normal and the reversed order. In the following the Minimax winner for the ballots in normalorder is determined. The results...
misunderstood. However, German's flexible word order allows one to emphasise specific words: Normal word order: Der Direktor betrat gestern um 10 Uhr mit...
reductions are possible. Normal-order reduction is complete, in the sense that if a term has a head normal form, then normal‐order reduction will eventually...
of first-order logic is in Skolem normal form if it is in prenex normal form with only universal first-order quantifiers. Every first-order formula may...
normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution...
for a normal distribution. The theoretical quantiles are generally chosen to approximate either the mean or the median of the corresponding order statistics...
as regular order, regular orders, and the like can refer to: Regular order (United States Congress), a process of governance Normalorder (disambiguation)...
A normal mode of a dynamical system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed...
the normal maps must be able to reflect the new orientation without computationally expensive updates to texture data in the transform. In order to find...
square matrix A is normal if it commutes with its conjugate transpose A*: A normal ⟺ A ∗ A = A A ∗ . {\displaystyle A{\text{ normal}}\iff A^{*}A=AA^{*}...
an approximation, to the expectation of the order statistic of the same rank in a sample of standard normal random variables of the same size as the observed...
In linear algebra, a Jordan normal form, also known as a Jordan canonical form, is an upper triangular matrix of a particular form called a Jordan matrix...
In mathematics, a real number is said to be simply normal in an integer base b if its infinite sequence of digits is distributed uniformly in the sense...
A normal school or normal college is an institution created to train teachers by educating them in the norms of pedagogy and curriculum. Many such schools...
religious order; promote anarchy; and, echoing with the Dalai clique, encourage separatist activities, sabotage Tibet's stability, damage the normalorder of...
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