Knowledge (XXG)

Infrared divergence

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analysis, shows that an infinite number of soft photons are created. But only a finite number are detectable, the remainder, due to their low energy, falling below any finite energy detection threshold, which must necessarily exist. However even though most of the photons are not detectable they
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and take the limit as the cutoff approaches zero and/or refine the question. Another way is to assign the massless particle a fictitious mass, and then take the limit as the fictitious mass vanishes.
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The divergence is usually in terms of particle number and not empirically troubling, in that all measurable quantities remain finite. (Unlike in the case of the
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states with a finite number of photons vanishes. Finite transition amplitudes are obtained only by summing over states with an infinite number of soft photons.
431: 274: 233: 120:, there will be an infinite number of particles in order to have a finite amount of energy. One way to deal with it is to impose an 460: 455: 450: 424: 168: 144: 199: 152: 148: 128: 417: 194: 350: 303: 157: 63:). They represent a legitimate effect that a complete theory often implies. In fact, in the case of 266: 255: 397: 366: 319: 270: 229: 56: 401: 70: 358: 311: 184: 189: 140: 121: 99: 40: 47:
approaching zero, or equivalently, because of physical phenomena at very long distances.
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is the frequency associated to the particle and as it goes to zero, like in the case of
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in the coaccelerated frame in which the charge experiences a thermal bath due to the
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can't be ignored in the theory; quantum electrodynamic calculations show that the
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Higuchi, A.; Matsas, G. E. A.; Sudarsky, D. (1992-10-15).
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Higuchi, A.; Matsas, G. E. A.; Sudarsky, D. (1992-05-15).
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The zero-energy photons become important in analyzing the
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The infrared divergence only appears in theories with
102: 73: 254: 108: 88: 292:"Bremssstrahlung and zero-energy Rindler photons" 425: 8: 253:Claude Itzykson, Jean-Bernard Zuber (1980). 226:Quantum Field Theory: A Modern Introduction 432: 418: 143:is accelerated (or decelerated) it emits 101: 72: 211: 219: 217: 215: 131:where the energies involved diverge.) 228:. New York: Oxford University Press. 16:Type of diverging integral in physics 7: 386: 384: 248: 246: 404:. You can help Knowledge (XXG) by 14: 388: 240:, pages 177-184 and appendix A6 1: 35:) is a situation in which an 477: 383: 316:10.1103/PhysRevD.45.R3308 67:, the energy is given by 363:10.1103/PhysRevD.46.3450 169:Bremsstrahlung radiation 145:Bremsstrahlung radiation 89:{\displaystyle E=h\nu } 400:-related article is a 200:Ultraviolet divergence 153:quantum electrodynamic 149:electromagnetic theory 135:Bremsstrahlung example 110: 90: 461:Quantum physics stubs 456:Renormalization group 224:Kaku, Michio (1993). 195:Renormalization group 111: 91: 451:Quantum field theory 257:Quantum Field Theory 158:transition amplitude 109:{\displaystyle \nu } 100: 71: 33:infrared catastrophe 355:1992PhRvD..46.3450H 308:1992PhRvD..45.3308H 302:(10): R3308–R3311. 25:infrared divergence 106: 86: 57:massless particles 413: 412: 398:quantum mechanics 343:Physical Review D 296:Physical Review D 468: 434: 427: 420: 392: 385: 375: 374: 349:(8): 3450–3457. 334: 328: 327: 287: 281: 280: 260: 250: 241: 239: 221: 185:Cutoff (physics) 147:. Semiclassical 115: 113: 112: 107: 95: 93: 92: 87: 39:, for example a 476: 475: 471: 470: 469: 467: 466: 465: 441: 440: 439: 438: 381: 379: 378: 336: 335: 331: 289: 288: 284: 277: 252: 251: 244: 236: 223: 222: 213: 208: 190:Renormalization 181: 141:electric charge 137: 122:infrared cutoff 98: 97: 69: 68: 53: 41:Feynman diagram 17: 12: 11: 5: 474: 472: 464: 463: 458: 453: 443: 442: 437: 436: 429: 422: 414: 411: 410: 393: 377: 376: 329: 282: 275: 242: 234: 210: 209: 207: 204: 203: 202: 197: 192: 187: 180: 177: 151:, or the full 136: 133: 129:UV catastrophe 105: 85: 82: 79: 76: 52: 49: 15: 13: 10: 9: 6: 4: 3: 2: 473: 462: 459: 457: 454: 452: 449: 448: 446: 435: 430: 428: 423: 421: 416: 415: 409: 407: 403: 399: 394: 391: 387: 382: 372: 368: 364: 360: 356: 352: 348: 344: 340: 333: 330: 325: 321: 317: 313: 309: 305: 301: 297: 293: 286: 283: 278: 276:0-07-032071-3 272: 268: 264: 259: 258: 249: 247: 243: 237: 235:0-19-507652-4 231: 227: 220: 218: 216: 212: 205: 201: 198: 196: 193: 191: 188: 186: 183: 182: 178: 176: 174: 170: 165: 163: 159: 154: 150: 146: 142: 134: 132: 130: 125: 123: 119: 103: 83: 80: 77: 74: 66: 62: 58: 50: 48: 46: 42: 38: 34: 30: 29:IR divergence 26: 22: 406:expanding it 395: 380: 346: 342: 332: 299: 295: 285: 256: 225: 173:Unruh effect 166: 161: 138: 126: 118:soft photons 54: 32: 28: 24: 18: 265:. pp.  263:McGraw-Hill 445:Categories 206:References 104:ν 84:ν 59:(such as 371:10015290 324:10014292 179:See also 160:between 139:When an 96:, where 51:Overview 37:integral 351:Bibcode 304:Bibcode 65:photons 61:photons 21:physics 369:  322:  273:  232:  45:energy 27:(also 396:This 267:172/3 23:, an 402:stub 367:PMID 320:PMID 271:ISBN 230:ISBN 359:doi 312:doi 162:any 31:or 19:In 447:: 365:. 357:. 347:46 345:. 341:. 318:. 310:. 300:45 298:. 294:. 269:. 261:. 245:^ 214:^ 433:e 426:t 419:v 408:. 373:. 361:: 353:: 326:. 314:: 306:: 279:. 238:. 81:h 78:= 75:E

Index

physics
integral
Feynman diagram
energy
massless particles
photons
photons
soft photons
infrared cutoff
UV catastrophe
electric charge
Bremsstrahlung radiation
electromagnetic theory
quantum electrodynamic
transition amplitude
Bremsstrahlung radiation
Unruh effect
Cutoff (physics)
Renormalization
Renormalization group
Ultraviolet divergence



ISBN
0-19-507652-4


Quantum Field Theory
McGraw-Hill

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