{ "schema_version": 1, "kind": "ConceptView", "producer": "concept-view-1", "concept_id": "urn:uuid:4f2153cc-eb69-4a7d-ba5c-eabaf46627e6", "labels": { "zh-CN": "Wiener测度", "en": "Wiener measure" }, "alternative_labels": [], "scope_note": "", "identity_status": "active", "identity_revision": "10ac38f3961d23765d45b3a4deee869c92196aac4831bd3a32cac15ebd990816", "occurrences": [ { "concept_id": "urn:uuid:4f2153cc-eb69-4a7d-ba5c-eabaf46627e6", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "zh-CN", "route": "books/woit-qtgr/2025-10-20/zh/chapter-35/03-quantization-and-path-integrals", "anchor": "first-bf33b2fb096561412dd4-zh", "chapter": "35", "section": "35.3", "offset": 7991, "range": [ 15569, 15873 ], "source_revision": "c20845fbbd9a4da88711f6c72719b5b0d5a50c91e0038cd383c78d66f47dc88a", "source_category": "machine_draft", "review_status": "machine-draft-not-reviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "Wiener测度(Wiener measure)", "context": { "range": [ 15444, 15978 ], "quote": "使路径积分定义得更好的一种方法是在时间变量中进行解析延拓，正如在 12.5 节中对自由粒子情形所讨论的那样。在这种自由粒子情形中，在位置空间路径积分的定义中，用方程 12.8 代替方程 12.9 的使用，人们发现这导致路径上有一个定义良好的测度，即[Wiener测度(Wiener measure)](../../../../../concepts/probability/wiener-measure)。更一般地，当势能非零时，可以使用维纳测度技术来定义路径积分，得到的结果最终需要解析延拓回物理时间变量。", "quote_sha256": "750f5df78fc3506df1c7c4ef60a4c13c3422a7162c6464f039253c5f03b24c72", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-35/03-quantization-and-path-integrals", "lang": "en", "source_category": "machine_draft", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-c1a7b23af2f021ba3ec4e7ac" }, { "concept_id": "urn:uuid:4f2153cc-eb69-4a7d-ba5c-eabaf46627e6", "book_id": "woit-qtgr", "edition_id": "2025-10-20", "lang": "en", "route": "books/woit-qtgr/2025-10-20/en/chapter-35/03-quantization-and-path-integrals", "anchor": "first-bf33b2fb096561412dd4-en", "chapter": "35", "section": "35.3", "offset": 13980, "range": [ 20718, 21012 ], "source_revision": "2336c369bd577a395279cba6824210a156a2fc4bb1ead9bd8094200e4cd0817b", "source_category": "machine_draft", "review_status": "machine-draft-not-reviewed", "role": "occurrence", "role_basis": { "kind": "explicit-source-uuid-marker" }, "label": "Wiener measure", "context": { "range": [ 19816, 21289 ], "quote": "One method for making path integrals better defined is an analytic continuation in the time variable, as discussed in section 12.5 for the case of a free particle. In such a free particle case, replacing the use of equation 12.9 by equation 12.8 in the definition of the position space path integral, one finds that this leads to a well-defined measure on paths, [Wiener measure](../../../../../concepts/probability/wiener-measure). More generally, Wiener measure techniques can be used to define the path integral when the potential energy is non-zero, getting results that ultimately need to be analytically continued back to the physical time variable.", "quote_sha256": "84693202994b7e3f31f379d0d8df6d66ca574896a1d4d90f75fe1d24a2bf438d", "environment": null, "excerpt_omitted": false }, "parallel_readings": [ { "route": "books/woit-qtgr/2025-10-20/zh/chapter-35/03-quantization-and-path-integrals", "lang": "zh-CN", "source_category": "machine_draft", "basis": "registered-book-edition-section-language-context; not-concept-equivalence" } ], "id": "occ-54549ad947a9dc8045fce42f" } ], "registered_positions": [ { "route": "books/woit-qtgr/2025-10-20/en/chapter-35/03-quantization-and-path-integrals", "lang": "en", "section": "35.3", "signal": "term-mark", "label": "Wiener measure", "english": "Wiener measure", "offset": 13216 }, { "route": "books/woit-qtgr/2025-10-20/zh/chapter-35/03-quantization-and-path-integrals", "lang": "zh-CN", "section": "35.3", "signal": "term-mark", "label": "Wiener测度", "english": "Wiener measure", "offset": 7227 } ], "statements": [], "resolved_references": [ { "raw": "href=\"../chapter-12/05-the-propagator-in-position-space#section-12-5\"", "href": "../chapter-12/05-the-propagator-in-position-space#section-12-5", "range": [ 19937, 20006 ], "relation": "references", "target_route": "books/woit-qtgr/2025-10-20/en/chapter-12/05-the-propagator-in-position-space", "target_anchor": "section-12-5", "resolved": true, "reason": null, "source_revision": "2336c369bd577a395279cba6824210a156a2fc4bb1ead9bd8094200e4cd0817b", "source_route": "books/woit-qtgr/2025-10-20/en/chapter-35/03-quantization-and-path-integrals", "occurrence_id": "occ-54549ad947a9dc8045fce42f" }, { "raw": "href=\"../chapter-12/05-the-propagator-in-position-space#equation-12-9\"", "href": "../chapter-12/05-the-propagator-in-position-space#equation-12-9", "range": [ 20212, 20282 ], "relation": "references", "target_route": "books/woit-qtgr/2025-10-20/en/chapter-12/05-the-propagator-in-position-space", "target_anchor": "equation-12-9", "resolved": true, "reason": null, "source_revision": "2336c369bd577a395279cba6824210a156a2fc4bb1ead9bd8094200e4cd0817b", "source_route": "books/woit-qtgr/2025-10-20/en/chapter-35/03-quantization-and-path-integrals", "occurrence_id": "occ-54549ad947a9dc8045fce42f" }, { "raw": "href=\"../chapter-12/05-the-propagator-in-position-space#equation-12-8\"", "href": "../chapter-12/05-the-propagator-in-position-space#equation-12-8", "range": [ 20409, 20479 ], "relation": "references", "target_route": "books/woit-qtgr/2025-10-20/en/chapter-12/05-the-propagator-in-position-space", "target_anchor": "equation-12-8", "resolved": true, "reason": null, "source_revision": "2336c369bd577a395279cba6824210a156a2fc4bb1ead9bd8094200e4cd0817b", "source_route": "books/woit-qtgr/2025-10-20/en/chapter-35/03-quantization-and-path-integrals", "occurrence_id": "occ-54549ad947a9dc8045fce42f" } ], "reading_order": [ "occ-c1a7b23af2f021ba3ec4e7ac", "occ-54549ad947a9dc8045fce42f" ], "recorded_dependencies": [], "reading_paths": [], "coverage": { "registered_positions": 2, "located_occurrences": 2, "whole_book_search_complete": false, "registered_positions_truncated": false, "independent_human_review_implied": false }, "unresolved": [], "base_revision": "f475b7b7e3fd9c41c5847e1a7965755eda89a40d0f823d78badd06344a71d687", "optional_enrichments": [] }