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T. Filk, "Divergences in a field theory on Quantum Space," Phys. Lett. B 376, 53 (1996); A. Connes, M.R. Douglas, and A. Schwarz, "Noncommutative geometry and matrix Theory: compactification on tori," J. High Energy Phys. 02, 003 (1998); N. Seiberg and E. Witten, "String theory and noncommutative geometry," ibid. 032, 9909 (1999); A. Matusis, L. Susskind, and N. Toumbas, "The IR/UV connection in non-commutative Gauge Theories," hep-th/0002075; O. Andreev and H. Dorn, "Diagrams of noncommutative phi-three theory from string Theory," hep-th/0003113; Y. Kiem and S. Lee, "UV/IV mixing in noncommutative field theory via open string Loops," hep-th/0003145; A. Bilal, C.-S. Chu, and R. Russo, "String theory and noncommutative field theories at One-loop," hep-th/0003180; J. Gomis, M. Kleban, T. Mehen, M. Rangamani, and S. Shenker, "Noncommutative gauge dynamics from the string worldsheet," hep-th/0003215; H. Liu and J. Michelson, "Stretched strings in noncommutative field theory," hep-th/0004013.
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T. Filk, "Divergences in a field theory on Quantum Space," Phys. Lett. B 376, 53 (1996); A. Connes, M.R. Douglas, and A. Schwarz, "Noncommutative geometry and matrix Theory: compactification on tori," J. High Energy Phys. 02, 003 (1998); N. Seiberg and E. Witten, "String theory and noncommutative geometry," ibid. 032, 9909 (1999); A. Matusis, L. Susskind, and N. Toumbas, "The IR/UV connection in non-commutative Gauge Theories," hep-th/0002075; O. Andreev and H. Dorn, "Diagrams of noncommutative phi-three theory from string Theory," hep-th/0003113; Y. Kiem and S. Lee, "UV/IV mixing in noncommutative field theory via open string Loops," hep-th/0003145; A. Bilal, C.-S. Chu, and R. Russo, "String theory and noncommutative field theories at One-loop," hep-th/0003180; J. Gomis, M. Kleban, T. Mehen, M. Rangamani, and S. Shenker, "Noncommutative gauge dynamics from the string worldsheet," hep-th/0003215; H. Liu and J. Michelson, "Stretched strings in noncommutative field theory," hep-th/0004013.
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T. Filk, "Divergences in a field theory on Quantum Space," Phys. Lett. B 376, 53 (1996); A. Connes, M.R. Douglas, and A. Schwarz, "Noncommutative geometry and matrix Theory: compactification on tori," J. High Energy Phys. 02, 003 (1998); N. Seiberg and E. Witten, "String theory and noncommutative geometry," ibid. 032, 9909 (1999); A. Matusis, L. Susskind, and N. Toumbas, "The IR/UV connection in non-commutative Gauge Theories," hep-th/0002075; O. Andreev and H. Dorn, "Diagrams of noncommutative phi-three theory from string Theory," hep-th/0003113; Y. Kiem and S. Lee, "UV/IV mixing in noncommutative field theory via open string Loops," hep-th/0003145; A. Bilal, C.-S. Chu, and R. Russo, "String theory and noncommutative field theories at One-loop," hep-th/0003180; J. Gomis, M. Kleban, T. Mehen, M. Rangamani, and S. Shenker, "Noncommutative gauge dynamics from the string worldsheet," hep-th/0003215; H. Liu and J. Michelson, "Stretched strings in noncommutative field theory," hep-th/0004013.
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T. Filk, "Divergences in a field theory on Quantum Space," Phys. Lett. B 376, 53 (1996); A. Connes, M.R. Douglas, and A. Schwarz, "Noncommutative geometry and matrix Theory: compactification on tori," J. High Energy Phys. 02, 003 (1998); N. Seiberg and E. Witten, "String theory and noncommutative geometry," ibid. 032, 9909 (1999); A. Matusis, L. Susskind, and N. Toumbas, "The IR/UV connection in non-commutative Gauge Theories," hep-th/0002075; O. Andreev and H. Dorn, "Diagrams of noncommutative phi-three theory from string Theory," hep-th/0003113; Y. Kiem and S. Lee, "UV/IV mixing in noncommutative field theory via open string Loops," hep-th/0003145; A. Bilal, C.-S. Chu, and R. Russo, "String theory and noncommutative field theories at One-loop," hep-th/0003180; J. Gomis, M. Kleban, T. Mehen, M. Rangamani, and S. Shenker, "Noncommutative gauge dynamics from the string worldsheet," hep-th/0003215; H. Liu and J. Michelson, "Stretched strings in noncommutative field theory," hep-th/0004013.
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T. Filk, "Divergences in a field theory on Quantum Space," Phys. Lett. B 376, 53 (1996); A. Connes, M.R. Douglas, and A. Schwarz, "Noncommutative geometry and matrix Theory: compactification on tori," J. High Energy Phys. 02, 003 (1998); N. Seiberg and E. Witten, "String theory and noncommutative geometry," ibid. 032, 9909 (1999); A. Matusis, L. Susskind, and N. Toumbas, "The IR/UV connection in non-commutative Gauge Theories," hep-th/0002075; O. Andreev and H. Dorn, "Diagrams of noncommutative phi-three theory from string Theory," hep-th/0003113; Y. Kiem and S. Lee, "UV/IV mixing in noncommutative field theory via open string Loops," hep-th/0003145; A. Bilal, C.-S. Chu, and R. Russo, "String theory and noncommutative field theories at One-loop," hep-th/0003180; J. Gomis, M. Kleban, T. Mehen, M. Rangamani, and S. Shenker, "Noncommutative gauge dynamics from the string worldsheet," hep-th/0003215; H. Liu and J. Michelson, "Stretched strings in noncommutative field theory," hep-th/0004013.
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T. Filk, "Divergences in a field theory on Quantum Space," Phys. Lett. B 376, 53 (1996); A. Connes, M.R. Douglas, and A. Schwarz, "Noncommutative geometry and matrix Theory: compactification on tori," J. High Energy Phys. 02, 003 (1998); N. Seiberg and E. Witten, "String theory and noncommutative geometry," ibid. 032, 9909 (1999); A. Matusis, L. Susskind, and N. Toumbas, "The IR/UV connection in non-commutative Gauge Theories," hep-th/0002075; O. Andreev and H. Dorn, "Diagrams of noncommutative phi-three theory from string Theory," hep-th/0003113; Y. Kiem and S. Lee, "UV/IV mixing in noncommutative field theory via open string Loops," hep-th/0003145; A. Bilal, C.-S. Chu, and R. Russo, "String theory and noncommutative field theories at One-loop," hep-th/0003180; J. Gomis, M. Kleban, T. Mehen, M. Rangamani, and S. Shenker, "Noncommutative gauge dynamics from the string worldsheet," hep-th/0003215; H. Liu and J. Michelson, "Stretched strings in noncommutative field theory," hep-th/0004013.
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T. Filk, "Divergences in a field theory on Quantum Space," Phys. Lett. B 376, 53 (1996); A. Connes, M.R. Douglas, and A. Schwarz, "Noncommutative geometry and matrix Theory: compactification on tori," J. High Energy Phys. 02, 003 (1998); N. Seiberg and E. Witten, "String theory and noncommutative geometry," ibid. 032, 9909 (1999); A. Matusis, L. Susskind, and N. Toumbas, "The IR/UV connection in non-commutative Gauge Theories," hep-th/0002075; O. Andreev and H. Dorn, "Diagrams of noncommutative phi-three theory from string Theory," hep-th/0003113; Y. Kiem and S. Lee, "UV/IV mixing in noncommutative field theory via open string Loops," hep-th/0003145; A. Bilal, C.-S. Chu, and R. Russo, "String theory and noncommutative field theories at One-loop," hep-th/0003180; J. Gomis, M. Kleban, T. Mehen, M. Rangamani, and S. Shenker, "Noncommutative gauge dynamics from the string worldsheet," hep-th/0003215; H. Liu and J. Michelson, "Stretched strings in noncommutative field theory," hep-th/0004013.
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String theory and noncommutative field theories at One-loop
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T. Filk, "Divergences in a field theory on Quantum Space," Phys. Lett. B 376, 53 (1996); A. Connes, M.R. Douglas, and A. Schwarz, "Noncommutative geometry and matrix Theory: compactification on tori," J. High Energy Phys. 02, 003 (1998); N. Seiberg and E. Witten, "String theory and noncommutative geometry," ibid. 032, 9909 (1999); A. Matusis, L. Susskind, and N. Toumbas, "The IR/UV connection in non-commutative Gauge Theories," hep-th/0002075; O. Andreev and H. Dorn, "Diagrams of noncommutative phi-three theory from string Theory," hep-th/0003113; Y. Kiem and S. Lee, "UV/IV mixing in noncommutative field theory via open string Loops," hep-th/0003145; A. Bilal, C.-S. Chu, and R. Russo, "String theory and noncommutative field theories at One-loop," hep-th/0003180; J. Gomis, M. Kleban, T. Mehen, M. Rangamani, and S. Shenker, "Noncommutative gauge dynamics from the string worldsheet," hep-th/0003215; H. Liu and J. Michelson, "Stretched strings in noncommutative field theory," hep-th/0004013.
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Noncommutative gauge dynamics from the string worldsheet
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T. Filk, "Divergences in a field theory on Quantum Space," Phys. Lett. B 376, 53 (1996); A. Connes, M.R. Douglas, and A. Schwarz, "Noncommutative geometry and matrix Theory: compactification on tori," J. High Energy Phys. 02, 003 (1998); N. Seiberg and E. Witten, "String theory and noncommutative geometry," ibid. 032, 9909 (1999); A. Matusis, L. Susskind, and N. Toumbas, "The IR/UV connection in non-commutative Gauge Theories," hep-th/0002075; O. Andreev and H. Dorn, "Diagrams of noncommutative phi-three theory from string Theory," hep-th/0003113; Y. Kiem and S. Lee, "UV/IV mixing in noncommutative field theory via open string Loops," hep-th/0003145; A. Bilal, C.-S. Chu, and R. Russo, "String theory and noncommutative field theories at One-loop," hep-th/0003180; J. Gomis, M. Kleban, T. Mehen, M. Rangamani, and S. Shenker, "Noncommutative gauge dynamics from the string worldsheet," hep-th/0003215; H. Liu and J. Michelson, "Stretched strings in noncommutative field theory," hep-th/0004013.
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Stretched strings in noncommutative field theory
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It can be argued that if noncommutativity exists in phase-space, the *-genvalue equation is more fundamental than the Schrödinger equation. This is so because in the Schrödinger equation, the wave functions are in position space alone, hence one has to define the action of the momentum operator on them, while in the *-genvalue problem the only necessary information comes from the commutation relations and is encoded in the *-product.
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