# Modification of Energy-Momentum Relation and UV/IR mixing

>From a seminar, I heard that energy-momentum relation (E^2=m^2+p^2) is
modified by UV/IR mxing.
In other words, the speaker claimed that the lowest energy is achived
not by zero momentum, but by non-zero momentum. Could somebody refer
me to a relevant paper?

Youngsub

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Igor Khavkine
On May 3, 5:20 pm, [email protected] wrote:
> From a seminar, I heard that energy-momentum relation (E^2=m^2+p^2) is
> modified by UV/IR mxing.
> In other words, the speaker claimed that the lowest energy is achived
> not by zero momentum, but by non-zero momentum. Could somebody refer
> me to a relevant paper?

Sorry, I'm not sure I can refer you to immediately relevant papers.
The concept of UV/IR mixing that I've seen came up in the context of
non-commutative field theory. That is, field theory defined on a space-
time where coordinates do not commute. A standard reference for
physicists is a paper by Douglass & Nekrasov [1]. The mathematical
principles of non-commutative spaces are founded in the non-
commutative geometry of Alain Connes [2]. You may find some useful
information in these references.

Hope this helps.

Igor

[1] Douglass & Nekrasov, Noncommutative field theory,
Rev. Mod. Phys. 73, pp.977-1029 (2001)
[2] Connes, Noncommutative Geometry, Academic Press (1994)