{"_buckets": {"deposit": "e25ae528-f5f7-4611-bfa0-2f3fe6e19436"}, "_deposit": {"id": "2005317", "owners": [1], "pid": {"revision_id": 0, "type": "depid", "value": "2005317"}, "status": "published"}, "_oai": {"id": "oai:u-ryukyu.repo.nii.ac.jp:02005317", "sets": ["1642837633191", "1642838406414"]}, "author_link": [], "item_1617186331708": {"attribute_name": "Title", "attribute_value_mlt": [{"subitem_1551255647225": "Proper time as an operator", "subitem_1551255648112": "en"}]}, "item_1617186419668": {"attribute_name": "Creator", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "Matsumoto, Shuichi", "creatorNameLang": "en"}]}, {"creatorNames": [{"creatorName": "\u677e\u672c, \u4fee\u4e00", "creatorNameLang": "ja"}]}]}, "item_1617186476635": {"attribute_name": "Access Rights", "attribute_value_mlt": [{"subitem_1522299639480": "open access", "subitem_1600958577026": "http://purl.org/coar/access_right/c_abf2"}]}, "item_1617186626617": {"attribute_name": "Description", "attribute_value_mlt": [{"subitem_description": "When we quantize a system consisting of a single particle, the proper time \u03c4 and the rest mass m are usually dealt with as parameters. In the present article, however, we introduce a new quantization rule by which these quantities are regarded as operators in addition to the position and the momentum. Applying this new rule to a scalar particle and to a particle with spin 1/2, we analyze the time evolution of the operator \u03c4. In the former case, the evolution of the proper time perfectly matches several well-established classical formulae. In the case of the particle with spin 1/2, our new rule implies that an oscillation appears in the time evolution of the operator \u03c4. This oscillation is similar to Zitterbewegung which is well-known in the ordinary Dirac theory. We formulate one physical effect of this oscillation by considering the interaction with a gravitational field, and estimate how small it is.", "subitem_description_type": "Other"}, {"subitem_description": "\u7d00\u8981\u8ad6\u6587", "subitem_description_type": "Other"}]}, "item_1617186643794": {"attribute_name": "Publisher", "attribute_value_mlt": [{"subitem_1522300295150": "en", "subitem_1522300316516": "Department of Mathematical Sciences, Faculty of Science, University of the Ryukyus"}]}, "item_1617186702042": {"attribute_name": "Language", "attribute_value_mlt": [{"subitem_1551255818386": "eng"}]}, "item_1617186783814": {"attribute_name": "Identifier", "attribute_value_mlt": [{"subitem_identifier_type": "HDL", "subitem_identifier_uri": "http://hdl.handle.net/20.500.12000/15167"}]}, "item_1617186920753": {"attribute_name": "Source Identifier", "attribute_value_mlt": [{"subitem_1522646500366": "ISSN", "subitem_1522646572813": "1344-008X"}, {"subitem_1522646500366": "NCID", "subitem_1522646572813": "AA10779580"}]}, "item_1617186941041": {"attribute_name": "Source Title", "attribute_value_mlt": [{"subitem_1522650068558": "en", "subitem_1522650091861": "Ryukyu mathematical journal"}]}, "item_1617187056579": {"attribute_name": "Bibliographic Information", "attribute_value_mlt": [{"bibliographicPageEnd": "51", "bibliographicPageStart": "37", "bibliographicVolumeNumber": "12"}]}, "item_1617258105262": {"attribute_name": "Resource Type", "attribute_value_mlt": [{"resourcetype": "departmental bulletin paper", "resourceuri": "http://purl.org/coar/resource_type/c_6501"}]}, "item_1617265215918": {"attribute_name": "Version Type", "attribute_value_mlt": [{"subitem_1522305645492": "VoR", "subitem_1600292170262": "http://purl.org/coar/version/c_970fb48d4fbd8a85"}]}, "item_1617605131499": {"attribute_name": "File", "attribute_type": "file", "attribute_value_mlt": [{"accessrole": "open_access", "download_preview_message": "", "file_order": 0, "filename": "Vol12p037.pdf", "future_date_message": "", "is_thumbnail": false, "mimetype": "", "size": 0, "url": {"objectType": "fulltext", "url": "https://u-ryukyu.repo.nii.ac.jp/record/2005317/files/Vol12p037.pdf"}, "version_id": "a63ea1fa-174f-4413-a4b1-74abdf011dad"}]}, "item_title": "Proper time as an operator", "item_type_id": "15", "owner": "1", "path": ["1642837633191", "1642838406414"], "permalink_uri": "http://hdl.handle.net/20.500.12000/15167", "pubdate": {"attribute_name": "PubDate", "attribute_value": "2010-01-26"}, "publish_date": "2010-01-26", "publish_status": "0", "recid": "2005317", "relation": {}, "relation_version_is_last": true, "title": ["Proper time as an operator"], "weko_shared_id": -1}