Space/time non-commutativity and causality

By N. Seiberg, L. Susskind, N. Toumbas. 2000

248 citations recorded by the source corpus.

Field theories based on non-commutative spacetimes exhibit very distinctive non-local effects which mix the ultraviolet with the infrared in bizarre ways. In particular if the time coordinate is involved in the non-commutativity the theory seems to be seriously acausal and inconsistent with conventional hamiltonian evolution. To illustrate these effects we study the scattering of wave packets in a field theory with space/time non-commutativity. In this theory we find effects which seem to precede their causes and rigid rods which grow instead of Lorentz contract as they are boosted. These field theories are evidently inconsistent and violate causality and unitarity. On the other hand open string theory in a background electric field is expected to exhibit space/time non-commutativity. This raises the question of whether they also lead to acausal behavior. We show that this is not the case. Stringy effects conspire to cancel the acausal effects that are present for the non-commutative field theory.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/21a0086bfa0b334e3bbf74bc5738b9dc9c04e750

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. N. Seiberg
2. Rajesh Gopakumar
3. O. Aharony
4. J. Maldacena
5. E. Witten
6. Andrew Strominger
7. Shiraz Minwalla
8. U. Danielsson

In Nuclear and High Energy Physics

1. J. Maldacena
2. N. Seiberg
3. Joaquim Gomis
4. Rajesh Gopakumar
5. O. Aharony
6. E. Witten
7. Shiraz Minwalla
8. Andrew Strominger

In Statistical and Nonlinear Physics

1. J. Maldacena
2. Joaquim Gomis
3. Andrew Strominger
4. N. Seiberg
5. E. Witten
6. Shiraz Minwalla
7. Rajesh Gopakumar
8. R. Szabo

Citations in the corpus

• On theories with light-like noncommutativity (2000, background): “However, field theories on such spaces exhibit acausal behaviour [4,5] and the quantum theories are not unitary [6].”
• OM theory in diverse dimensions (2000, methodology): “As the name NCOS theory (Non-Commutative Open String) indicates, they exhibit non-commutativity of space and time coordinates (spacetime noncommutativity was also considered in [4,5,6,7,8] .”
• Dipoles, Twists and Noncommutative Gauge Theory (2000, background): “Timelike noncommutativity [22] appears to require inclusion of stringy degrees of freedom [23]-[30],[32].”
• S-Duality and Noncommutative Gauge Theory (2000, background): “Investigations to date have largely concentrated on theories with purely spatial noncommutativity (see however [2]).”
• IIA/B, wound and wrapped (2000, background): “Such theories have a peculiar space/time non-commutativity(1) which in principle threatens their consistency [8, 9, 10].”
• Quantum field theory on noncommutative spaces (2001, background): “ with noncommuting time direction, i.e. θ0i6= 0, one encounters severe acausal effects, such as events which precede their causes and objects which grow instead of Lorentz contract as they are boosted [83]. Such a quantum field theory is neither causal nor unitary in certain instances [84]. In a theor”