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This is an audio version of the Wikipedia Article:\nhttps://en.wikipedia.org/wiki/Noncommutative_quantum_field_theory\n\n\n00:02:12 1 History and motivation
00:06:25 2 See also
00:06:47 3 Footnotes
00:06:56 4 Further reading
\n\n\nListening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.\n\nLearning by listening is a great way to:\n- increases imagination and understanding\n- improves your listening skills\n- improves your own spoken accent\n- learn while on the move\n- reduce eye strain\n\nNow learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.\n\nListen on Google Assistant through Extra Audio:\nhttps://assistant.google.com/services/invoke/uid/0000001a130b3f91\nOther Wikipedia audio articles at:\nhttps://www.youtube.com/results?search_query=wikipedia+tts\nUpload your own Wikipedia articles through:\nhttps://github.com/nodef/wikipedia-tts\nSpeaking Rate: 0.7350565790871001\nVoice name: en-GB-Wavenet-B\n\n\n"I cannot teach anybody anything, I can only make them think."\n- Socrates\n\n\nSUMMARY\n=======\nIn mathematical physics, noncommutative quantum field theory (or quantum field theory on noncommutative spacetime) is an application of noncommutative mathematics to the spacetime of quantum field theory that is an outgrowth of noncommutative geometry and index theory in which the coordinate functions are noncommutative. One commonly studied version of such theories has the "canonical" commutation relation:




[

x

μ


,

x

ν


]
=
i

θ

μ
ν






{\displaystyle [x^{\mu },x^{\nu }]=i\theta ^{\mu \nu }\,\!}
which means that (with any given set of axes), it is impossible to accurately measure the position of a particle with respect to more than one axis. In fact, this leads to an uncertainty relation for the coordinates analogous to the Heisenberg uncertainty principle.
Various lower limits have been claimed for the noncommutative scale, (i.e. how accurately positions can be measured) but there is currently no experimental evidence in favour of such a theory or grounds for ruling them out.
One of the novel features of noncommutative field theories is the UV/IR mixing phenomenon in which the physics at high energies affects the physics at low energies which does not occur in quantum field theories in which the coordinates commute.
Other features include violation of Lorentz invariance due to the preferred direction of noncommutativity. Relativistic invariance can however be retained in the sense of twisted Poincaré invariance of the theory. The causality condition is modified from that of the commutative theories.