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Dimensional transmutation

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25: 318: 42: 191:, and its value 220 MeV supplants the role of the original dimensionless coupling constant in the form of the logarithm (at one-loop) of the ratio 359: 297: 89: 61: 108: 68: 388: 383: 46: 75: 378: 57: 352: 302: 203:. Perturbation theory, which produced this type of running formula, is only valid for a (dimensionless) coupling 35: 180: 141: 345: 165: 82: 268: 244: 325: 276: 272: 153: 329: 157: 122: 179:, namely the value of the RG scale at which the coupling constant diverges. In the case of 212: 372: 169: 130: 156:
is a dimensionless constant. However, upon quantization, logarithmic divergences in
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of perturbation theory imply that this "constant" actually depends on the typical
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Consequently, the interaction may be characterised by a dimensionful parameter
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From Current Algebra to Quantum Chromodynamics: A Case for Structural Realism
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broken upon quantization, thereby setting up a mass scale. See
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On the other hand, in the case of theories such as QED,
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is a physical mechanism providing a linkage between a
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Physical mechanism creating dimensionful parameters
164:of the processes under considerations, called the 353: 8: 360: 346: 207:≪ 1. In the case of QCD, the energy scale 109:Learn how and when to remove this message 288: 267:This is also a way of saying that the 7: 314: 312: 47:adding citations to reliable sources 332:. You can help Knowledge (XXG) by 14: 316: 23: 34:needs additional citations for 172:of the renormalization group. 1: 271:of the classical theory is 58:"Dimensional transmutation" 405: 311: 303:Cambridge University Press 127:dimensional transmutation 328:-related article is a 181:quantum chromodynamics 142:classical field theory 389:Quantum physics stubs 384:Renormalization group 166:renormalization group 379:Quantum field theory 183:, this energy scale 148:in four-dimensional 43:improve this article 269:conformal symmetry 245:ultraviolet cutoff 341: 340: 326:quantum mechanics 277:conformal anomaly 158:one-loop diagrams 154:coupling constant 119: 118: 111: 93: 396: 362: 355: 348: 320: 313: 306: 293: 263: 256: 242: 235: 231: 224: 210: 206: 202: 196: 186: 178: 133:parameter and a 123:particle physics 114: 107: 103: 100: 94: 92: 51: 27: 19: 404: 403: 399: 398: 397: 395: 394: 393: 369: 368: 367: 366: 310: 309: 294: 290: 285: 258: 248: 240: 236:the RG scale. 233: 226: 216: 213:infrared cutoff 208: 204: 198: 192: 184: 176: 115: 104: 98: 95: 52: 50: 40: 28: 17: 12: 11: 5: 402: 400: 392: 391: 386: 381: 371: 370: 365: 364: 357: 350: 342: 339: 338: 321: 308: 307: 295:Cao, Tian Yu. 287: 286: 284: 281: 187:is called the 117: 116: 31: 29: 22: 15: 13: 10: 9: 6: 4: 3: 2: 401: 390: 387: 385: 382: 380: 377: 376: 374: 363: 358: 356: 351: 349: 344: 343: 337: 335: 331: 327: 322: 319: 315: 304: 300: 299: 292: 289: 282: 280: 278: 274: 270: 265: 261: 255: 251: 246: 237: 229: 223: 219: 214: 201: 195: 190: 182: 173: 171: 170:beta function 167: 163: 159: 155: 151: 147: 143: 138: 136: 132: 131:dimensionless 128: 124: 113: 110: 102: 99:February 2024 91: 88: 84: 81: 77: 74: 70: 67: 63: 60: –  59: 55: 54:Find sources: 48: 44: 38: 37: 32:This article 30: 26: 21: 20: 334:expanding it 323: 305:, 2010. 163. 296: 291: 266: 259: 253: 249: 247:, such that 238: 227: 221: 217: 215:, such that 199: 193: 174: 162:energy scale 146:gauge theory 139: 135:dimensionful 126: 120: 105: 96: 86: 79: 72: 65: 53: 41:Please help 36:verification 33: 273:anomalously 137:parameter. 373:Categories 283:References 144:, such as 69:newspapers 189:QCD scale 150:spacetime 257:implies 225:implies 232:, with 83:scholar 243:is an 211:is an 152:, the 85:  78:  71:  64:  56:  324:This 90:JSTOR 76:books 330:stub 197:and 62:news 262:≪ 1 230:≪ 1 140:In 121:In 45:by 375:: 301:. 279:. 264:. 252:≪ 220:≫ 125:, 361:e 354:t 347:v 336:. 260:g 254:Λ 250:μ 241:Λ 234:μ 228:g 222:Λ 218:μ 209:Λ 205:g 200:Λ 194:μ 185:Λ 177:Λ 112:) 106:( 101:) 97:( 87:· 80:· 73:· 66:· 39:.

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verification
improve this article
adding citations to reliable sources
"Dimensional transmutation"
news
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books
scholar
JSTOR
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particle physics
dimensionless
dimensionful
classical field theory
gauge theory
spacetime
coupling constant
one-loop diagrams
energy scale
renormalization group
beta function
quantum chromodynamics
QCD scale
infrared cutoff
ultraviolet cutoff
conformal symmetry
anomalously
conformal anomaly
From Current Algebra to Quantum Chromodynamics: A Case for Structural Realism

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